Holt CA Course 1

2-7 Equations in Two Variables

Preparation for AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

California Standards

Holt CA Course 1

2-7 Equations in Two Variables

Most movies shown in theaters are shot using film. The table shows the relationship between the duration of a movie in minutes and the length of the film in feet. Look for a pattern in the table.

Duration of a Movie (min)

Length of Film Needed (ft)

1 90

2 180

3 270

90(1) = 90

90(2) = 180

90(3) = 270

Holt CA Course 1

2-7 Equations in Two Variables

The length of the film in feet is 90 times the duration of a movie in minutes. An equation in two variables can represent this relationship.

Length in feet is 90 times duration in minutes.

Holt CA Course 1

2-7 Equations in Two VariablesExample 1: Writing Equations from Tables

x 3 4 5 6 7 10

y 12 16 20 24 28

y is 4 times x.

y = 4x

Compare x and y to find a pattern.Use the pattern to write an equation.

y = 4(10) Substitute 10 for x.

y = 40Use your equation to find y when x = 10.

Write an equation in two variables that gives the values in the table. Use your equation to find the value of y for the indicated value of x.

Holt CA Course 1

2-7 Equations in Two Variables

When all the y-values are greater than the corresponding x-values, try using addition or multiplication of a positive integer in your equation.

Helpful Hint

Holt CA Course 1

2-7 Equations in Two Variables

You can write equations in two variables for relationships that are described in words.

Holt CA Course 1

2-7 Equations in Two Variables

Example 2: Translating Words into Math

The height of a painting is 7 times its width.

h = height of painting Choose variables for the equation.

h = 7w Write an equation.

Write an equation for the relationship. Tell what each variable you use represents.

w = width of painting

Holt CA Course 1

2-7 Equations in Two Variables

The school choir tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $80 for 20 tickets, $88 for 22 tickets, and $108 for 27 tickets. Write an equation for the relationship.

11 Understand the Problem

The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

Example 3: Problem Solving Application

Holt CA Course 1

2-7 Equations in Two Variables

You can make a table to display the data.22 Make a Plan

Solve33

Let t be the number of tickets. Let m be the amount of money received.

t 20 22 27

m 80 88 108

m is equal to 4 times t. Compare t and m.

m = 4t Write an equation.

Holt CA Course 1

2-7 Equations in Two Variables

Substitute the t and m values in the table to check that they are solutions of the equation m = 4t.

Look Back44

m = 4t (20, 80)

80 = 4 • 20?

80 = 80?

m = 4t (22, 88)

88 = 4 • 22?

88 = 88?

m = 4t (27, 108)

108 = 4 • 27?

108 = 108?

Holt CA Course 1

2-7 Equations in Two Variables Check It Out! Example 1

x 3 4 5 6 7 10

y 5 6 7 8 9

y is 2 more than x

y = x + 2

Compare x and y to find a pattern.Use the pattern to write an equation.

y = 10 + 2 Substitute 10 for x.

y = 12Use your equation to find y when x = 10.

Write an equation in two variables that gives the values in the table. Use the equation to find the value of y for the indicated value of x.

Holt CA Course 1

2-7 Equations in Two Variables

Check It Out! Example 2

The height of a mirror is 4 times its width.

h = height of mirrorChoose variables for the equation.

h = 4w Write an equation.

Write an equation for the relationship. Tell what each variable you use represents.

w = width of mirror

Holt CA Course 1

2-7 Equations in Two Variables

The school theater tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $45 for 15 tickets, $63 for 21 tickets, and $90 for 30 tickets. Write an equation for the function.

11 Understand the Problem

The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

Check It Out! Example 3

Holt CA Course 1

2-7 Equations in Two Variables

You can make a table to display the data.22 Make a Plan

Solve33

Let t be the number of tickets. Let m be the amount of money received.

t 15 21 30

m 45 63 90

m is equal to 3 times t. Compare t and m.

m = 3t Write an equation.

Holt CA Course 1

2-7 Equations in Two Variables

Substitute the t and m values in the table to check that they are solutions of the equation m = 3t.

Look Back44

m = 3t (15, 45)

45 = 3 • 15?

45 = 45?

m = 3t (21, 63)

63 = 3 • 21?

63 = 63?

m = 3t (30, 90)

90 = 3 • 30?

90 = 90?