1. Do Now: Pass out calculators.
Pick up an Algebra I sheet from the back – work on Mac & Tolley’s Road Trip problem.

2. Objective:
To solve a system of equations using substitution.

3. Use the substitution method
EXAMPLE 1
Use the substitution method
Solve the linear system:
y = 3x + 2
Equation 1
x + 2y = 11
Equation 2
SOLUTION
STEP 1
Solve for y. Equation 1 is already solved for y.

4. Use the substitution method
EXAMPLE 1
Use the substitution method
STEP 2
Substitute 3x + 2 for y in Equation 2 and solve for x.
x + 2y = 11
Write Equation 2.
x + 2(3x + 2) = 11
Substitute 3x + 2 for y.
7x + 4 = 11
Simplify.
7x = 7
Subtract 4 from each side.
x = 1
Divide each side by 7.

5. EXAMPLE 1
Use the substitution method
STEP 3
Substitute 1 for x in the original Equation 1 to find the value of y.
y = 3x + 2 = 3(1) + 2 = = 5
ANSWER
The solution is (1, 5).

6. Use the substitution method
EXAMPLE 1
GUIDED PRACTICE
Use the substitution method
CHECK
Substitute 1 for x and 5 for y in each of the original
equations.
y = 3x + 2
x + 2y = 11
5 = 3(1) + 2 ?
1 + 2 (5) = 11 ?
5 = 5
11 = 11

7. 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
STEP 1
Solve Equation 1 for x.
x – 2y = –6
Write original Equation 1.
x = 2y – 6
Revised Equation 1

8. Use the substitution method
EXAMPLE 2
Use the substitution method
STEP 2
Substitute 2y – 6 for x in Equation 2 and solve for y.
4x + 6y = 4
Write Equation 2.
4(2y – 6) + 6y = 4
Substitute 2y – 6 for x.
8y – y = 4
Distributive property
14y – 24 = 4
Simplify.
14y = 28
Add 24 to each side.
y = 2
Divide each side by 14.

9. Use the substitution method
EXAMPLE 2
Use the substitution method
STEP 3
Substitute 2 for y in the revised Equation 1 to find the value of x.
x = 2y – 6
Revised Equation 1
x = 2(2) – 6
Substitute 2 for y.
x = –2
Simplify.
ANSWER
The solution is (–2, 2).

10. Use the substitution method
EXAMPLE 2
GUIDED PRACTICE
Use the substitution method
CHECK
Substitute –2 for x and 2 for y in each of the original
equations.
Equation 1
Equation 2
4x + 6y = 4
x – 2y = –6
–2 – 2(2) = –6 ?
4(–2) + 6 (2) = 4 ?
–6 = –6
4 = 4

11. EXAMPLE 1
GUIDED PRACTICE
Use the substitution method
for Examples 1 and 2
Solve the linear system using the substitution method.
y = 2x + 5 1.
3x + y = 10
ANSWER
(1, 7)

12. EXAMPLE 2
GUIDED PRACTICE
Use the substitution method
for Examples 1 and 2
Solve the linear system using the substitution method.
x – y = 3 2.
x + 2y = –6
ANSWER
(0, –3)

13. EXAMPLE 2
GUIDED PRACTICE
Use the substitution method
for Examples 1 and 2
Solve the linear system using the substitution method.
3x + y = –7 3.
–2x + 4y = 0
ANSWER
(–2, –1)

14. 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.

15. 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
y = x

16. Solve a multi-step problem
EXAMPLE 3
Solve a multi-step problem
Equation 2: Website hosting company
y = x
The system of equations is:
y = x
Equation 1
y = 22.45x
Equation 2

17. Solve a multi-step problem
EXAMPLE 3
Solve a multi-step problem
STEP 2
Substitute 22.45x for y in Equation 1 and solve
for x.
y = x
Write Equation 1.
22.45x = x
Substitute 22.45x for y.
0.5x = 10
Subtract 21.95x from each side.
x = 20
Divide each side by 0.5.
The total cost will be the same for both companies after 20 months.
ANSWER