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