If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Digital SAT Math

### Course: Digital SAT Math>Unit 2

Lesson 6: Systems of linear equations word problems: foundations

# Systems of linear equations word problems | Lesson

A guide to systems of linear equations word problems on the digital SAT

## What are systems of linear equations word problems?

Systems of linear equations word problems ask us to translate real-world scenarios into a system of two linear equations with two variables. Often, we'll also be asked to solve the system.
This lesson builds upon an understanding of the following skills:
• Understanding linear relationships
• Solving systems of linear equations
You can learn anything. Let's do this!

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

### Systems of equations examples

Systems of equations with elimination: apples and orangesSee video transcript
Systems of equations with substitution: coinsSee video transcript

### How do I write systems of linear equations?

Word problems that require us to write systems of linear equations have two unknown quantities and two different ways to relate them.
This means we need to write two linear equations, and each contains the two unknowns as variables. The Understanding linear relationships lesson details how to translate verbal descriptions into equations.
After we write the equations, we can solve the system using our preferred method(s) for solving systems of linear equations covered in the Solving systems of linear equations lesson.
To solve a system of linear equations word problem:
1. Select variables to represent the unknown quantities.
2. Using the given information, write a system of two linear equations relating the two variables.
3. Solve the system of linear equations using either substitution or elimination.

#### Let's look at an example!

A theater production charges dollar sign, 21 for adult tickets and dollar sign, 15 for student tickets. If the production sold 102 tickets for its opening night and made dollar sign, 1, comma, 932 in ticket sales, how many of each type of tickets were sold?

### Try it!

Try: translate a scenario into equations
The player of a trivia game receives 100 points for each correct answer and loses 25 points for each incorrect answer. Leona answered a total of 30 questions and scored a total of 2, comma, 125 points.
Write an equation that relates the total number of questions Leona answered to C, the number of questions she answered correctly and I, the number of questions she answered incorrectly.
equals, 30
Leona received 100 points for each correct answer. Write an expression for the number of points she received from answering C questions correctly.
Because Leona loses 25 points for each incorrect answer, the quantity 25, I should be
Write an equation that models the total number of points Leona scored using C and I.
equals, 2, comma, 125

Practice: write a system of linear equations
At Beans & Bagels, a bagel costs dollar sign, 1 more than a cup of coffee. If 4 cups of coffee and 6 bagels cost dollar sign, 31, which of the following systems of equations can be used to determine the price of a bagel, b, and the price of a cup of coffee, c ?