case study

solve for x and y math problems

Sciencing_Icons_Science SCIENCE

Sciencing_icons_biology biology, sciencing_icons_cells cells, sciencing_icons_molecular molecular, sciencing_icons_microorganisms microorganisms, sciencing_icons_genetics genetics, sciencing_icons_human body human body, sciencing_icons_ecology ecology, sciencing_icons_chemistry chemistry, sciencing_icons_atomic & molecular structure atomic & molecular structure, sciencing_icons_bonds bonds, sciencing_icons_reactions reactions, sciencing_icons_stoichiometry stoichiometry, sciencing_icons_solutions solutions, sciencing_icons_acids & bases acids & bases, sciencing_icons_thermodynamics thermodynamics, sciencing_icons_organic chemistry organic chemistry, sciencing_icons_physics physics, sciencing_icons_fundamentals-physics fundamentals, sciencing_icons_electronics electronics, sciencing_icons_waves waves, sciencing_icons_energy energy, sciencing_icons_fluid fluid, sciencing_icons_astronomy astronomy, sciencing_icons_geology geology, sciencing_icons_fundamentals-geology fundamentals, sciencing_icons_minerals & rocks minerals & rocks, sciencing_icons_earth scructure earth structure, sciencing_icons_fossils fossils, sciencing_icons_natural disasters natural disasters, sciencing_icons_nature nature, sciencing_icons_ecosystems ecosystems, sciencing_icons_environment environment, sciencing_icons_insects insects, sciencing_icons_plants & mushrooms plants & mushrooms, sciencing_icons_animals animals, sciencing_icons_math math, sciencing_icons_arithmetic arithmetic, sciencing_icons_addition & subtraction addition & subtraction, sciencing_icons_multiplication & division multiplication & division, sciencing_icons_decimals decimals, sciencing_icons_fractions fractions, sciencing_icons_conversions conversions, sciencing_icons_algebra algebra, sciencing_icons_working with units working with units, sciencing_icons_equations & expressions equations & expressions, sciencing_icons_ratios & proportions ratios & proportions, sciencing_icons_inequalities inequalities, sciencing_icons_exponents & logarithms exponents & logarithms, sciencing_icons_factorization factorization, sciencing_icons_functions functions, sciencing_icons_linear equations linear equations, sciencing_icons_graphs graphs, sciencing_icons_quadratics quadratics, sciencing_icons_polynomials polynomials, sciencing_icons_geometry geometry, sciencing_icons_fundamentals-geometry fundamentals, sciencing_icons_cartesian cartesian, sciencing_icons_circles circles, sciencing_icons_solids solids, sciencing_icons_trigonometry trigonometry, sciencing_icons_probability-statistics probability & statistics, sciencing_icons_mean-median-mode mean/median/mode, sciencing_icons_independent-dependent variables independent/dependent variables, sciencing_icons_deviation deviation, sciencing_icons_correlation correlation, sciencing_icons_sampling sampling, sciencing_icons_distributions distributions, sciencing_icons_probability probability, sciencing_icons_calculus calculus, sciencing_icons_differentiation-integration differentiation/integration, sciencing_icons_application application, sciencing_icons_projects projects, sciencing_icons_news news.

  • Share Tweet Email Print
  • Home ⋅
  • Math ⋅
  • Algebra ⋅
  • Linear Equations

How to Solve for Both X & Y

To solve for x, you must perform the same operations on both sides of the equation.

How to Solve a System of Equations

Solving for two variables (normally denoted as "x" and "y") requires two sets of equations. Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.

Write out the two equations that have the two variables you want to solve. For this example, we will find the value for "x" and "y" in the two equations "3x + y = 2" and "x + 5y = 20"

Solve for one of the variables in on one of the equations. For this example, let's solve for "y" in the first equation. Subtract 3x from each side to get "y = 2 - 3x"

Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes "x + 5(2- 3x) = 20"

Solve for x . The example equation becomes "x + 10 - 15x = 20," which is then "-14 x + 10 = 20." Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.

Plug in the x value in to the first equation to find out the y value. y = 2 - 3(-5/7) becomes 2 + 15/7, which is 29/7.

Check your work by plugging in the x and y values in to both of the equations.

Related Articles

How to solve a parabola, how to solve linear systems algebraically, how to use elimination to solve the linear equation, how to find equations of tangent lines, how to graph and find the solution on a calculator, how to find the x intercept of a function, how to create linear equations, how do i define two step equations for algebra 2, to calculate arcsine, what buttons do you press on..., how to find dimensions in geometric shapes, how to find the y-intercept of a circle, how to get the value of a letter in algebra 1, how to find an ordered pair from an equation, how to find the slope in a circle, what is the definition of a common solution in college..., how to find the intersection of two linear equations, how to solve inequalities.

About the Author

Drew Lichtenstein started writing in 2008. His articles have appeared in the collegiate newspaper "The Red and Black." He holds a Master of Arts in comparative literature from the University of Georgia.

Photo Credits

BananaStock/BananaStock/Getty Images

Find Your Next Great Science Fair Project! GO

We Have More Great Sciencing Articles!

Algebra Calculator

What do you want to calculate.

Examples: 1+2 , 1/3+1/4 , 2^3 * 2^2   (x+1)(x+2) (Simplify Example), 2x^2+2y @ x=5, y=3 (Evaluate Example)   y=x^2+1 (Graph Example), 4x+2=2(x+6) (Solve Example)

Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples »

solve for x and y math problems

Disclaimer: This calculator is not perfect. Please use at your own risk, and please alert us if something isn't working. Thank you.

How to Use the Calculator

Type your algebra problem into the text box.

For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14.

solve for x and y math problems

More Examples

Calculator Examples »

Math Symbols

If you would like to create your own math expressions, here are some symbols that the calculator understands:

Calculator Tutorial »

Get the MathPapa mobile app! It works offline!

solve for x and y math problems

Feedback (For students 13+)

Please use this feedback form to send your feedback. Thanks!

Need more practice problems? Try MathPapa Math Practice

Get Premium

More Examples »

Back to Algebra Calculator »

Share this page

... and beyond

Search icon

How do you solve for #x# and #y# in the simultaneous equations #x + 2y = 3# and #x^2 - y^2 = 24#?

solve for x and y math problems

Hope this helped!

Related questions

Impact of this question

solve for x and y math problems

How to Solve Systems of Algebraic Equations Containing Two Variables

Last Updated: February 10, 2023 References

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 61 people, some anonymous, worked to edit and improve it over time. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 958,618 times. Learn more...

In a "system of equations," you are asked to solve two or more equations at the same time. When these have two different variables in them, such as x and y, or a and b, it can be tricky at first glance to see how to solve them. [1] X Research source Fortunately, once you know what to do, all you need is basic algebra skills (and sometimes some knowledge of fractions) to solve the problem. If you are a visual learner or if your teacher requires it, learn how to graph the equations as well. Graphing can be useful to "see what's going on" or to check your work, but it can be slower than the other methods, and doesn't work well for all systems of equations.

Using the Substitution Method

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 1

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 2

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 3

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 4

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 5

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 6

Using the Elimination Method

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 7

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 9

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 10

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 11

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 12

Graphing the Equations

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 13

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 14

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 15

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 16

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 17

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 18

Image titled Solve Systems of Algebraic Equations Containing Two Variables Step 19

Practice Problems and Answers

solve for x and y math problems

Community Q&A

Donagan

Video . By using this service, some information may be shared with YouTube.

solve for x and y math problems

You Might Also Like

Find the Maximum or Minimum Value of a Quadratic Function Easily

About This Article

To solve systems of algebraic equations containing two variables, start by moving the variables to different sides of the equation. Then, divide both sides of the equation by one of the variables to solve for that variable. Next, take that number and plug it into the formula to solve for the other variable. Finally, take your answer and plug it into the original equation to solve for the other variable. To learn how to solve systems of algebraic equations using the elimination method, scroll down! Did this summary help you? Yes No

Did this article help you?

solve for x and y math problems

Featured Articles

Play FIFA 23 Career Mode

Trending Articles

Talk to a Girl in a Group

Watch Articles

Make Homemade Soup

Don’t miss out! Sign up for

wikiHow’s newsletter

Download on App Store

Download on App Store

The equations section of QuickMath allows you to solve and plot virtually any equation or system of equations. In most cases, you can find exact solutions to your equations. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. It also contains a number of special commands for dealing with quadratic equations.

The Solve command can be uses to solve either a single equation for a single unknown from the basic solve page or to simultaneously solve a system of many equations in many unknowns from the advanced solve page . The advanced command allows you to specify whether you want approximate numerical answers as well as exact ones, and how many digits of accuracy (up to 16) you require. It also allows you to eliminate certain variables from the equations.

Go to the Solve page

The Plot command, from the Graphs section, will plot any function of two variables. In order to plot a single function of x, go to the basic equation plotting page , where you can enter the equation and specify the upper and lower limits on x that you want the graph to be plotted for. The advanced plotting page allows you to plot up to 6 equations on the one graph, each with their own color. It also gives you control over such things as whether or not to show the axes, where the axes should be located, what the aspect ratio of the plot should be and what the range of the dependent variable should be. All equations can be given in the explicit y = f(x) form or the implicit g(x,y) = c form.

Go to the Equation Plotting page

The Quadratics page contains 13 separate commands for dealing with the most common questions concerning quadratics. It allows you to : factor a quadratic function (by two different methods); solve a quadratic equation by factoring the quadratic, using the quadratic formula or by completing the square; rewrite a quadratic function in a different form by completing the square; calculate the concavity, x-intercepts, y-intercept, axis of symmetry and vertex of a parabola; plot a parabola; calculate the discriminant of a quadratic equation and use the discriminant to find the number of roots of a quadratic equation. Each command generates a complete and detailed custom-made explanation of all the steps needed to solve the problem.

Go to the Quadratics page

Introduction to Equations

By an equation we mean a mathematical sentence that states that two algebraic expressions are equal. For example, a (b + c) =ab + ac, ab = ba, and x 2 -1 = (x-1)(x+1) are all equations that we have been using. We recall that we defined a variable as a letter that may be replaced by numbers out of a given set, during a given discussion. This specified set of numbers is sometimes called the replacement set. In this chapter we will deal with equations involving variables where the replacement set, unless otherwise specified, is the set of all real numbers for which all the expressions in the equation are defined.

If an equation is true after the variable has been replaced by a specific number, then the number is called a solution of the equation and is said to satisfy it. Obviously, every solution is a member of the replacement set. The real number 3 is a solution of the equation 2x-1 = x+2, since 2*3-1=3+2. while 1 is a solution of the equation (x-1)(x+2) = 0. The set of all solutions of an equation is called the solution set of the equation.

In the first equation above {3} is the solution set, while in the second example {-2,1} is the solution set. We can verify by substitution that each of these numbers is a solution of its respective equation, and we will see later that these are the only solutions.

A conditional equation is an equation that is satisfied by some numbers from its replacement set and not satisfied by others. An identity is an equation that is satisfied by all numbers from its replacement set.

Example 1 Consider the equation 2x-1 = x+2

The replacement set here is the set of all real numbers. The equation is conditional since, for example, 1 is a member of the replacement set but not of the solution set.

Example 2 Consider the equation (x-1)(x+1) =x 2 -1 The replacement set is the set of all real numbers. From our laws of real numbers if a is any real number, then (a-1)(a+1) = a 2 -1 Therefore, every member of the replacement set is also a member of the solution set. Consequently this equation is an identity.  

solve for x and y math problems

The replacement set for this equation is the set of real numbers except 0, since 1/x and (1- x)/x are not defined for x = 0. If a is any real number in the replacement set, then

solve for x and y math problems

Math Topics

More solvers.

Math Practice

Algebra Solutions

Our goal here is to introduce some of the equation solving techniques that may be helpful for kids in understanding Algebra.

We start here with a very simple technique.

Let us say that there is an equation x + 3 = 9 and we need to solve it. Solving an equation means that we need to know the possible values of the variables that when put into the equation will satisfy it. We present the solution next.

Explanation:.

x + 3 = 9 (original equation ) x = 9 – 3 (take the constant term to the other side so that the variable x is isolated.) x = 6

So x = 6 is the required solution to the equation.

You have an equation 3x = 9. Find x.

3x = 9 (original equation) x = 9/3 (take the constant term associated with x to the other side so that the variable x is isolated.) x = 3

So x = 3 is the required solution to the equation.

We have two simultaneous equations in two variables x and y. Find x and y. x – y = 10 --------(1) x + y = 15 --------(2)

  (25/2, 5/2).

In solving these equations, we use a simple Algebraic technique called " Substitution Method ". In this method, we evaluate one of the variable value in terms of the other variable using one of the two equations. And that value is put into the second equation to solve for the two unknown values.

The solution below will make the idea of Substitution clear.

Using 1 st equation,

x – y = 10 -----(1) x = 10 + y

Now we put this value of x into the 2 nd equation.

x + y = 15 -----(2) (10 + y) + y = 15 10 + 2y = 15 2y = 15 – 10 = 5 y = 5/2

Putting this value of y into any of the two equations will give us the value of x.

x + y = 15 x + 5/2 = 15 x = 15 – 5/2 x = 25/2

Hence (x , y) = (25/2, 5/2) is the solution to the given system of equations.

We have two simultaneous equations in two variables x and y and we need to find x and y. x – y = 10 -----(1) x + y = 15 -----(2)

 (25/2, 5/2).

In Elimination Method, our aim is to "eliminate" one variable by making the coefficients of that variable equal and then adding/subtracting the two equations, depending on the case.

In this example, we see that the coefficients of all the variable are same, i.e., 1. So if we add the two equations, the –y and the +y will cancel each other giving as an equation in only x. Let me illustrate this below.

x – y = 10 x + y = 15 2x = 25 x = 25/2

Putting the value of x into any of the two equations will give y = 5/2

Elimination Method - By Equating Coefficients:

This is another very easy and useful equation solving technique that is extensively used in Algebraic calculations. We illustrate this method through an example.

Given two equations in two variables x and y. Find the values of x and y that satisfy these equations simultaneously. 2x – y = 10 ------(1) x + 2y = 15 ------(2)

 ( 7, 4).

In this example, we see that neither the coefficients of x nor those of y are equal in the two equations. So simple addition and subtraction will not lead to a simplified equation in only one variable. However, we can multiply a whole equation with a coefficient (say we multiply equation (2) with 2) to equate the coefficients of either of the two variables.

After multiplication, we get

2x + 4y = 30 ------(2)'

Next we subtract this equation (2)’ from equation (1)

2x – y = 10 2x + 4y = 30 –5y = –20 y = 4

Putting this value of y into equation (1) will give us the correct value of x.

2x – y = 10 ------(1) 2x – 4 = 10 2x = 10 + 4 = 14 x = 14/2 = 7

Hence (x , y) =( 7, 4) gives the complete solution to these two equations.

Different Equation Types

In Algebra , sometimes you may come across equations of the form Ax + B = Cx + D where x is the variable of the equation, and A,B,C,D are coefficient values (can be both positive and negative).

In the next section, we present an example of this type of equation and learn how to solve it through simple Algebraic techniques.

How to find system of linear equations using Simple Algebric techniques

Find a value of x that satisfies this equation: 4x – 3 = 3x + 8.

We are given that

4x – 3 = 3x + 8

Separating the variables and the coefficients gives:

4x – 3x = 8 + 3

(Note: Taking a constant or a variable term to the left hand side from the right hand side (or vice versa) changes its sign as illustrated above.)

Simplifying the above equation on the L.H.S (Left Hand Side) and the R.H.S (Right Hand Side) gives

Hence x = 11 is the required solution to the above equation.

In the equation A x + B = C x + D , the coefficients A, B, C, D may also be any decimal numbers. For example, the equation could be of this form: 4x + 3.2 = 6.1x + 5.2 -- But you are not supposed to be confused with the method. There will be no change in the equation solving strategy and once you have learnt the above method, you do not need to bother about the coefficients at all.

Next we present and try to solve the examples in a more detailed step-by-step approach. Examples given next are similar to those presented above and have been shown in a way that is more understandable for kids.

Solve x + 4 = 11 to find the value of x.

x + 4 – 4 = 11 – 4 x = 7

Hence x = 7 is the solution to the given equation.

How to solve system of Linear Equations by Elimination

Solve the following system using elimination. 2x + y = 15 3x – y = 10,  (5, 5).

If we use the method of addition in solving these two equations, we can see that what we get is a simplified equation in one variable, as shown below.

2x + y = 15 ------(1) 3x – y = 10 ------(2) ______________ 5x = 25

What we are left with is a simplified equation in x alone. i.e., 5x = 25

5x/5 = 25/5 x = 5

2(5) + y = 15 10 + y = 15

Which is another equation in a single variable y.

10 + y – 10 = 15 – 10 y = 5

Hence the solution to the system of equations is (x , y) = (5, 5)

Solve the following system using Elimination x + 2y = 15 x – y = 10

 ( 35/3 , 5/( 3 )).

With a little observation, we can conclude that if we directly add these two equations, we are not going to reach any simple equation. Let us show this below.

x + 2y = 15 ------(1) x – y = 10 ------(2) ______________ 2x + y = 25

Which is another equation in 2 variables x and y. So our problem doesn’t seem to have reduced. If instead of adding the two equations directly, I multiply the entire equation (1) with – 1, and then add the resulting equation into equation (2), the +x will be cancelled out with – x as shown next.

– ( x + 2y ) = – 15 – x – 2y = – 15 ------(1’)

– x – 2y = – 15 ------(1’) x – y = + 10 ------(2) ______________ – 3y = – 5

-3y/-3=-5/-3 y = 5/3

x – 5/3 = + 10

x – 5/3 + 5/3 = 10 + 5/3 x = (30+ 5)/3 = 35/3

Hence the solution to the given system of equations is (x , y) = ( 35/3 , 5/( 3 ))

Solve the following system of linear equations using Elimination. 8x – 13y = 2 –4x + 6.5y = –2

Apparently, this system seems to be a bit complex and one might think that no cancellation of terms is possible. But a close observation and a simple multiplication can lead us in the right direction.

We are given two equations:

8x – 13y = 2 ------(1) –4x + 6.5y = –2 ------(2)

2(–4x + 6.5y ) = 2(–2) –8x + 13y = –4 ------(2’)

8x – 13y = 2 ------(1) –8x + 13y = –4 ------(2’) ______________ 0 = –2

But this is not true!! 0≠ –2

Hence the two equations constitute an inconsistent system of linear equations and thus do no have a solution (At no point do the two straight lines intersect => No solution!)

How to solve system of Linear Equations by Substitution

Solve the following system of linear equations by substitution. 2x – 2y = –2 x + y = 24,  23/2 , 25/( 2 ).

In this method of equation solving, we work out on any of the given equations for one variable value, and then substitute that value in the other equation. It gives us an equation in a single variable and we can use a single variable equation solving technique to find the value of that variable (as shown in examples above). Let us solve the given system now

2x – 2y = –2 ------(1) x + y = 24 ------(2)

Now the next question is: which equation to pick up. There is no particular criteria for this choice. One can simply choose an equation that makes the calculations simpler. E.g., in this example, the equation (2) is easier to work on.

x + y = 24 ------(2)

2(24 – y) – 2y = –2 48 – 2y – 2y = –2 48 – 4y = – 2

48 – 4y – 48 = –2 –48 –4y = –50

-4y/-4 = -50/-4 y = 50/4 = 25/2

x + 25/2 = 24

x + 25/2 - 25/2 = 24 - 25/2 x = (48 - 25)/2 = 23/2

Hence the solution to the given system of equations is (x , y) = ( 23/2 , 25/( 2 ))

Note: Next we show what happens if we substitute the value of x into the same equation that we used to compute it (equation (2) in this example)

x + y = 24 24 – y + y = 24 ∵ (x = 24 – y) 24 = 24

This is the result that we are left with. There is nothing wrong with 24 being equal to 24, but then what should we do with it? Of course we have not been looking to prove this in the first place!!

Hence we conclude that there is no point in substituting the computed value into the same equation that was used for its computation. Always use the other equation!

Solve the following system of linear equations by method of substitution. y = 24 – 4x 2x + y/2 = 12

  y = 24 – 4x.

As shown in the above example, we compute the variable value from one equation and substitute it into the other.

y = 24 – 4x ------(1) 2x + y/2 = 12 ------(2)

Here we choose equation (1) to compute the value of x. Since equation (1) is already in its most simplified form:

(Putting this value of y into equation (2) and then solving for x gives)

2x + (24-4x)/2 = 12 ------(2) (∵ y = 24 – 4x) 2x + 24/2- 4x/2 = 12 2x + 12 – 2x = 12 12 = 12

You might feel that this is the same scenario as discussed above (that of 24 = 24). But wait! You are trying to jump at a conclusion a bit too early. In the previous scenario, the result 24 = 24 had resulted because we put the variable value into the same equation that we used for its computation. Here we have not done that.

The result 12 = 12 has got something to do with the nature of the system of equations that we are given. No matter what solving technique you might be using, a solution to a system of linear equations lies at a single point where their lines intersect. In this scenario, the two lines are basically the same (one line over the other. The following figure shows this scenario.

Such a system is called a dependent system of equations. And solution to such a system is the entire line (every point on the line is a point of intersection of the two lines)

Hence the solution to the given system of equations is the entire line: y = 24 – 4x

Another possible Scenario:

Similar to this example, there exists another scenario where substitution of one variable into the 2 nd equation leads to a result similar to one shown below:

Such a scenario arises when there exists no solution to the given system of equations. I.e., when the two lines do not intersect at any point at all.

Hence in case of such a result, where your basic Math rules seem to fail, a simple conclusion is that no solution to the given system exists. Such a system of equations is called an Inconsistent system.

Popular Algebra Links

Become a member today, are you a member sign in, math practice skills, math worksheets, monthly newsletter.

Subscribe to our newsletter and be the first to know about all updates!

iPracticeMath

Math practice

Terms of Use

Privacy policy

© 2023 iPracticeMath | All Rights Reserved | Terms of Use.

solve for x and y math problems

Solving an equation is the process of getting what you're looking for, or  solving for , on one side of the equals sign and everything else on the other side. You're really sorting information. If you're solving for  x , you must get x  on one side by itself.

Addition and subtraction equations

Some equations involve only addition and/or subtraction.

Solve for  x .

x  + 8 = 12

To solve the equation  x  + 8 = 12, you must get  x  by itself on one side. Therefore, subtract 8 from both sides.

solve for x and y math problems

To check your answer, simply plug your answer into the equation:

solve for x and y math problems

Solve for  y .

y  – 9 = 25

To solve this equation, you must get  y  by itself on one side. Therefore, add 9 to both sides.

solve for x and y math problems

To check, simply replace  y  with 34:

solve for x and y math problems

x  + 15 = 6

To solve, subtract 15 from both sides.

solve for x and y math problems

To check, simply replace  x  with –9 :

solve for x and y math problems

Notice that in each case above,  opposite operations  are used; that is, if the equation has addition, you subtract from each side.

Multiplication and division equations

Some equations involve only multiplication or division. This is typically when the variable is already on one side of the equation, but there is either more than one of the variable, such as 2  x , or a fraction of the variable, such as

solve for x and y math problems

In the same manner as when you add or subtract, you can multiply or divide both sides of an equation by the same number,  as long as it is not zero , and the equation will not change.

Divide each side of the equation by 3.

solve for x and y math problems

To check, replace  x  with 3:

solve for x and y math problems

To solve, multiply each side by 5.

solve for x and y math problems

To check, replace  y  with 35:

solve for x and y math problems

Or, without canceling,

solve for x and y math problems

Combinations of operations

Sometimes you have to use more than one step to solve the equation. In most cases, do the addition or subtraction step first. Then, after you've sorted the variables to one side and the numbers to the other, multiply or divide to get only one of the variables (that is, a variable with no number, or 1, in front of it:  x , not 2  x ).

2  x  + 4 = 10

Subtract 4 from both sides to get 2  x  by itself on one side.

solve for x and y math problems

Then divide both sides by 2 to get  x .

solve for x and y math problems

To check, substitute your answer into the original equation:

solve for x and y math problems

5x  – 11 = 29

Add 11 to both sides.

solve for x and y math problems

Divide each side by 5.

solve for x and y math problems

To check, replace  x  with 8:

solve for x and y math problems

Subtract 6 from each side.

solve for x and y math problems

To check, replace  x  with 9: 

solve for x and y math problems

Add 8 to both sides.

solve for x and y math problems

To check, replace  y  with –25: 

solve for x and y math problems

3  x  + 2 =  x  + 4

Subtract 2 from both sides (which is the same as adding –2).

solve for x and y math problems

Subtract  x  from both sides.

solve for x and y math problems

Note that 3  x  –  x  is the same as 3  x  – 1  x .

Divide both sides by 2.

solve for x and y math problems

To check, replace  x  with 1:

solve for x and y math problems

5  y  + 3 = 2  y  + 9

Subtract 3 from both sides.

solve for x and y math problems

Subtract 2  y  from both sides.

solve for x and y math problems

Divide both sides by 3.

solve for x and y math problems

To check, replace  y  with 2:

solve for x and y math problems

Sometimes you need to simplify each side (combine like terms) before actually starting the sorting process.

 Solve for  x .     

3  x  + 4 + 2 = 12 + 3

First, simplify each side.

solve for x and y math problems

Subtract 6 from both sides.

solve for x and y math problems

To check, replace  x  with 3: 

solve for x and y math problems

4  x  + 2  x  + 4 = 5  x  + 3 + 11

Simplify each side.

6  x  + 4 = 5  x  + 14

Subtract 4 from both sides.

solve for x and y math problems

Subtract 5  x  from both sides.

solve for x and y math problems

To check, replace  x  with 10: 

solve for x and y math problems

Previous Quiz: Variables and Algebraic Expressions

Next Quiz: Solving Simple Equations

has been added to your

Reading List!

Removing #book# from your Reading List will also remove any bookmarked pages associated with this title.

Are you sure you want to remove #bookConfirmation# and any corresponding bookmarks?

IMAGES

  1. Grade 12 mathematics on how to solve for x and y.

    solve for x and y math problems

  2. Algebra solve for x problems

    solve for x and y math problems

  3. Step by Step Solution for How to Solve X

    solve for x and y math problems

  4. Algebra 1: Lesson 1 Linear Equations: Equations with x and y (Simplifying Math)

    solve for x and y math problems

  5. solve this equation by any method x +y / xy = 2 x-y / xy

    solve for x and y math problems

  6. Math Expression: Graphing Quadratic Equation Practice Question 1

    solve for x and y math problems

VIDEO

  1. Sam is 10 yrs older than his sister. Next year he will be twice as old. How old is Sam now?

  2. Can You Solve This Problem in 60 Seconds

  3. Nice Algebra Problem

  4. Adding Radical Expressions #upcat #civilservicesexam #let #seniorhighschool

  5. What is the value of x/y? #knowledge #shorts #MNaumanAshraf #questionsolve #math #maths#mathematics

  6. Find x, y

COMMENTS

  1. Solving an equation for y and x

    Learn how to solve literal equations. A literal equation is an equation where the unknown values are represented by variables.

  2. Equations with x and y (Simplifying Math)

    Algebra 1 lesson about Linear Equations (Equations with x and y). This lesson shows how to transform and make a table of values for a linear

  3. How to Solve for Both X & Y

    Solving for two variables (normally denoted as "x" and "y") requires two sets of equations. Assuming you have two equations

  4. Math Practice Problems

    Solution x + 2y = 4 2x + y = 5. Multiply the second equation by 2 x + 2y = 4 4x + 2y = 10. Subtract the equations to eliminate y. · x + 2y = 4 - [ 4x + 2y = 10 ]

  5. Algebra Calculator

    Solves algebra problems and walks you through them. ... y=x^2+1. Disclaimer: This calculator is not perfect. ... problems? Try MathPapa Math Practice.

  6. How do you solve for x and y in the simultaneous equations x+2y=3

    The two solutions are (−7,5) and (5,−1) . Explanation: To solve the system of equations: {x+2y=3 (1)x2−y2=24 (2).

  7. 4 Ways to Solve Systems of Algebraic Equations Containing Two

    Using the Elimination Method · You have the system of equations 3x - y = 3 and -x + 2y = 4. · Let's change the first equation so that the y variable will cancel

  8. Solve equations and systems with Step-by-Step Math Problem Solver

    Solve an equation, inequality or a system. Example: 2x-1=y,2y+3=x. 1

  9. How to solve Algebra

    Hence (x , y) = (25/2, 5/2) is the solution to the given system of equations. Elimination Method - By Equating Coefficients: In Elimination Method, our aim is

  10. Solving Simple Equations

    To solve this equation, you must get y by itself on one side. Therefore, add 9 to both sides. To check, simply replace y with 34: Example 3.