7.2 Solve Linear Systems by Substitution

•Solve systems of linear equations by substitution.

•Determine what the “solution” means in a system of equations.

Solve the equation.

1. 6a – 3 + 2a = 13

2. 4(n + 2) – n = 11

ANSWER

ANSWER

3. You burned 8 calories per minute on a treadmilland 10 calories per minute on an elliptical trainer for a total of 560 calories in 60 minutes. How many minutes did you spend on each machine?

ANSWER

ANSWER

A pet store sells angel fish for $6 each and clown loaches for $4 each. If the pet store sold 8 fish for $36, how many of each type of fish did it sell?

3.

EXAMPLE 1 Use the substitution method

Solve the linear system:

y = 3x + 2

Equation 2

Equation 1

x + 2y = 11

SOLUTION

EXAMPLE 1 Use the substitution method

Substitute 3x + 2 for y in Equation 2 and solve for x.

STEP 2

EXAMPLE 1 Use the substitution method

ANSWER

Substitute 1 for x in the original Equation 1 to find the value of y.

STEP 3

GUIDED PRACTICE

CHECKSubstitute 1 for x and 5 for y in each of the original equations.

EXAMPLE 1 Use the substitution method

EXAMPLE 2 Use the substitution method

Solve the linear system:x – 2y = –6 Equation 1

4x + 6y = 4 Equation 2

SOLUTION

EXAMPLE 2 Use the substitution method

Substitute 2y – 6 for x in Equation 2 and solve for y.STEP 2

EXAMPLE 2 Use the substitution method

Substitute 2 for y in the revised Equation 1 to find the value of x.

ANSWER

STEP 3

GUIDED PRACTICE

CHECKSubstitute –2 for x and 2 for y in each of the original equations.

Equation 1 Equation 2

EXAMPLE 2 Use the substitution method

EXAMPLE 1 Use the substitution method

Solve the linear system using the substitution method.

3x + y = 10

y = 2x + 51.

GUIDED PRACTICE for Examples 1 and 2

ANSWER

EXAMPLE 2 Use the substitution method

–2x + 4y = 0

GUIDED PRACTICE for Examples 1 and 2

3x + y = –73.

Solve the linear system using the substitution method.

ANSWER

EXAMPLE 3 Solve a multi-step problem

Many businesses pay website hosting companies to store and maintain the computer files that make up their websites. Internet service providers also offer website hosting. The costs for website hosting offered by a website hosting company and an Internet service provider are shown in the table. Find the number of months after which the total cost for website hosting will be the same for both companies.

WEBSITES

21.00

22.00

Solve a multi-step problem

EXAMPLE 3

SOLUTION

Write a system of equations. Let y be the totalcost after x months.

Equation 1: Internet service provider

STEP 1

Solve a multi-step problem

EXAMPLE 3

Equation 2: Website hosting company

Solve a multi-step problem

EXAMPLE 3

Substitute 22.00x for y in Equation 1 and solvefor x.

STEP 2