## Writing Systems of Linear Equations from Word Problems

(i) There are two different quantities involved: for instance, the number of adults and the number of children, the number of large boxes and the number of small boxes, etc. (ii) There is a value associated with each quantity: for instance, the price of an adult ticket or a children's ticket, or the number of items in a large box as opposed to a small box.

Here are some steps to follow:

Understand all the words used in stating the problem. Understand what you are asked to find. Familiarize the problem situation.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Use substitution , elimination or graphing method to solve the problem.

The admission cost for 12 children and 3 adults was $ 162 . The admission cost for 8 children and 3 adults was $ 122 .

2 . Translate the problem to an equation.

Let x represent the admission cost for each child. Let y represent the admission cost for each adult. The admission cost for 12 children plus 3 adults is equal to $ 162 . That is, 12 x + 3 y = 162 . The admission cost for 8 children plus 3 adults is equal to $122. That is, 8 x + 3 y = 122 .

3 . Carry out the plan and solve the problem.

Subtract the second equation from the first. 12 x + 3 y = 162 8 x + 3 y = 122 _ 4 x = 40 x = 10 Substitute 10 for x in 8 x + 3 y = 122 . 8 ( 10 ) + 3 y = 122 80 + 3 y = 122 3 y = 42 y = 14 Therefore, the cost of admission for each child is $ 10 and each adult is $ 14 .

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## Unit 6: Lesson 3

- Solving linear equations and linear inequalities | Lesson
- Understanding linear relationships | Lesson
- Linear inequality word problems | Lesson
- Graphing linear equations | Lesson
- Systems of linear inequalities word problems | Lesson
- Solving systems of linear equations | Lesson

## Systems of linear equations word problems | Lesson

What are systems of linear equations word problems, and how frequently do they appear on the test.

## How do I solve systems of linear equations word problems?

Systems of equations examples, how do i write systems of linear equations.

- Select variables to represent the unknown quantities.
- Using the given information, write a system of two linear equations relating the two variables.
- Solve the system of linear equations using either substitution or elimination.

## Let's look at an example!

- (Choice A) c − 1 = b 4 b + 6 c = 31 \begin{aligned} c-1 &= b \\ \\ 4b+6c &=31 \end{aligned} c − 1 4 b + 6 c = b = 3 1 A c − 1 = b 4 b + 6 c = 31 \begin{aligned} c-1 &= b \\ \\ 4b+6c &=31 \end{aligned} c − 1 4 b + 6 c = b = 3 1
- (Choice B) c + 1 = b 4 b + 6 c = 31 \begin{aligned} c+1 &= b \\ \\ 4b+6c &=31 \end{aligned} c + 1 4 b + 6 c = b = 3 1 B c + 1 = b 4 b + 6 c = 31 \begin{aligned} c+1 &= b \\ \\ 4b+6c &=31 \end{aligned} c + 1 4 b + 6 c = b = 3 1
- (Choice C) c − 1 = b 6 b + 4 c = 31 \begin{aligned} c-1 &= b \\ \\ 6b+4c &=31 \end{aligned} c − 1 6 b + 4 c = b = 3 1 C c − 1 = b 6 b + 4 c = 31 \begin{aligned} c-1 &= b \\ \\ 6b+4c &=31 \end{aligned} c − 1 6 b + 4 c = b = 3 1
- (Choice D) c + 1 = b 6 b + 4 c = 31 \begin{aligned} c+1 &= b \\ \\ 6b+4c &=31 \end{aligned} c + 1 6 b + 4 c = b = 3 1 D c + 1 = b 6 b + 4 c = 31 \begin{aligned} c+1 &= b \\ \\ 6b+4c &=31 \end{aligned} c + 1 6 b + 4 c = b = 3 1
- (Choice A) 1 1 1 1 A 1 1 1 1
- (Choice B) 2 2 2 2 B 2 2 2 2
- (Choice C) 3 3 3 3 C 3 3 3 3
- (Choice D) 4 4 4 4 D 4 4 4 4
- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text

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## Solving Systems of Equations Real World Problems

## Steps For Solving Real World Problems

- Highlight the important information in the problem that will help write two equations.
- Define your variables
- Write two equations
- Use one of the methods for solving systems of equations to solve.
- Check your answers by substituting your ordered pair into the original equations.
- Answer the questions in the real world problems. Always write your answer in complete sentences!

## Example 1: Systems Word Problems

1. Let's start by identifying the important information:

Let x = the number of hot dogs sold

Let y = the number of sodas sold

1.50x + 0.50y = 78.50 (Equation related to cost)

x + y = 87 (Equation related to the number sold)

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6. Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7. Check your work by substituting.

Since both equations check properly, we know that our answers are correct!

## Example 2: Another Word Problem

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25 (Equation representing your lunch)

4x + 2y = 10 (Equation representing your friend's lunch)

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

## Take a look at the questions that other students have submitted:

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Systems problem about hats and scarves

How much did Alice spend on shoes?

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

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## Systems of Equations Word Problems Lesson

- Demonstrate an understanding of how to solve a System of Linear Equations in Two Variables
- Demonstrate an understanding of how to check the solution for a word problem
- Learn the six-step process used to solve a word problem with linear systems

## How to Solve Word Problems with Linear Systems

Six-step method for applications of linear systems.

- Read the problem, get a clear understanding of the objective
- Assign a variable to represent each unknown
- Write two equations using both variables
- Solve the linear system
- State the answer using a nice clear sentence
- Check the result by reading back through the problem

## Skills Check:

Please choose the best answer.

Better Luck Next Time, Your Score is %

Ready for more? Watch the Step by Step Video Lesson | Take the Practice Test

## Word Problems – System Of Equations

## Solving Word Problems

The y-values cancel each other out, so now you are left with only x-values and real numbers.

Then, you plug in your x-value into an original equation in order to find the y-value.

Cost of a cherry tree: $8 Cost of a rose bush: $12

## Examples of Word Problems – System Of Equations

Let’s solve this by following steps.

3. Use sentences to create equations.

Now, we have a system of equations:

High School A rented and filled 8 vans and 8 buses with 240 students.

High School B rented and filled 4 vans and 1 bus with 54 students.

## Video-Lesson Transcript

Let’s solve this by following steps above.

1. What we don’t know: cost of a cherry tree cost of a rose bush

Now, we have a system of equations

We can solve this by process of substitution, elimination or fraction.

Here we’ll have a negated equation

Let’s do the process of elimination now

Remember, our declared variable?

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## System-of-Equations Word Problems

## MathHelp.com

System of Equations Word Problems

With these variables, I can create equations for the totals they've given me:

total income: 4 a + 1.5 c = 5050

Now I can back-solve for the value of the other variable:

(new number) is (old number) increased by (twenty-seven)

10 u + 1 t = (10 t + 1 u ) + 27

Now I have a system of equations that I can solve:

First I'll simplify the second equation:

After reordering the variables in the first equation, I now have:

## How can I find a parabola's equation from just three points?

(But what does it look like when they give you not-nice points?)

Simplifying the three equations, I get:

You may also see similar exercises referring to circles, using:

−( 1 / 2 ) gt 2 + v 0 t + h 0 = s

URL: https://www.purplemath.com/modules/systprob.htm

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## Systems of Equations (Word Problems)

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- \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
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- \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}

## Frequently Asked Questions (FAQ)

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The word equation for cellular respiration is glucose (sugar) + oxygen = carbon dioxide + water + energy (as ATP). The balanced chemical equation for this reaction is C6H1206 + 6O2 = 6CO2 + 6H2O + energy (ATP).

In words, the equation for combustion, in most cases, is a hydrocarbon plus oxygen equals carbon dioxide plus water plus heat. Other cases involve burning hydrogen and oxygen without carbon and reactions that create carbon monoxide.

The word equation for neutralization is acid + base = salt + water. The acid neutralizes the base, and hence, this reaction is called a neutralization reaction. Neutralization leaves no hydrogen ions in the solution, and the pH of the solut...

Writing Systems of Linear Equations from Word Problems · 1. Understand the problem. Understand all the words used in stating the problem. Understand what you are

Systems of equations word problems example 1 | Algebra I | Khan Academy. Fundraiser.

Select variables to represent the unknown quantities. · Using the given information, write a system of two linear equations relating the two variables. · Solve

Solving Systems of Equations Real World Problems · Let x = the number of hot dogs sold · Let y = the number of sodas sold · 3. · One equation will be related to the

Read the problem, get a clear understanding of the objective · Assign a variable to represent each unknown · Write two equations using both variables · Solve the

An example on how to do this: Mary and Jose each bought plants from the same store. Mary spent $188 on 7 cherry trees and 11 rose bushes

Sometimes more than one equation is needed to model a given word problem. To solve the problem, you solve the system (i.e., the collection) of equations.

Example: A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters

solution · Step 1: Make sure the equations have opposite x terms or opposite y terms. · Step 2: Add to eliminate one variable and solve for the other. · Step 3:

6) All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7.

Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer. How do you identify