1. 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.

2. 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.

3. 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).

4. 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

5. 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

6. 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.

7. 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).

8. 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

9. 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)

10. 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)

11. 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)