Download 7.2 Solve Linear Systems by Substitution

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
ANSWER
2. 4(n + 2) – n = 11
ANSWER
3. You burned 8 calories per minute on a treadmill
and 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
3.
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?
ANSWER
EXAMPLE 1
Use the substitution method
Solve the linear system:
SOLUTION
y = 3x + 2
Equation 1
x + 2y = 11
Equation 2
EXAMPLE 1
Use the substitution method
STEP 2
Substitute 3x + 2 for y in Equation 2 and solve for x.
EXAMPLE 1
Use the substitution method
STEP 3
Substitute 1 for x in the original Equation 1 to find
the value of y.
ANSWER
EXAMPLE
1
Use the substitution method
GUIDED PRACTICE
CHECK
Substitute 1 for x and 5 for y in each of the original
equations.
EXAMPLE 2
Use the substitution method
Solve the linear system:
x – 2y = –6
4x + 6y = 4
SOLUTION
Equation 1
Equation 2
EXAMPLE 2
Use the substitution method
STEP 2
Substitute 2y – 6 for x in Equation 2 and solve for y.
EXAMPLE 2
Use the substitution method
STEP 3
Substitute 2 for y in the revised Equation 1 to find the
value of x.
ANSWER
EXAMPLE
2
Use the substitution method
GUIDED PRACTICE
CHECK
Substitute –2 for x and 2 for y in each of the original
equations.
Equation 1
Equation 2
EXAMPLE
1
for Examples
1 and 2
Use the substitution
method
GUIDED PRACTICE
Solve the linear system using the substitution method.
1.
y = 2x + 5
3x + y = 10
ANSWER
EXAMPLE
2
for Examples
1 and 2
Use the substitution
method
GUIDED PRACTICE
Solve the linear system using the substitution method.
3.
3x + y = –7
–2x + 4y = 0
ANSWER
EXAMPLE 3
Solve a multi-step problem
WEBSITES
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.
21.00
22.00
EXAMPLE 3
Solve a multi-step problem
SOLUTION
STEP 1
Write a system of equations. Let y be the total
cost after x months.
Equation 1: Internet service provider
EXAMPLE 3
Solve a multi-step problem
Equation 2: Website hosting company
EXAMPLE 3
Solve a multi-step problem
STEP 2
Substitute 22.00x for y in Equation 1 and solve
for x.