The substitution method is a technique for solving systems of linear equations by solving one equation for one variable in terms of the other and substituting it into the second equation. This allows you to solve the system by finding the value of one variable, substituting it into the first equation, and then solving for the remaining

1. 7.2 Solve Linear Systems by
Substitution
P. 435 - 441

2. • In this section, you will learn the second
method to solve a linear system. This
method is called SUBSTITUTION.
• This method is not a visual method (like
graph-&-check), but a quicker method to
find the solution.

3. Here are the steps to solve using Substitution
Method
1. Solve one of the equations for one of its
variables. (When possible, solve for a variable
that has a coefficient of 1 or -1).
2. Substitute the expression from Step 1 into the
OTHER equation and solve the for the other
variable.
3. Substitute the value from Step 2 into the
revised equation form Step 1 and solve.

4. 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.

5. 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.

6. 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 = 3 + 2 = 5
ANSWER
The solution is (1, 5).

7. EXAMPLE 1
GUIDED PRACTICE substitution method
Use the
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

8. 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

9. 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 – 24 + 6y = 4 Distributive property
14y – 24 = 4 Simplify.
14y = 28 Add 24 to each side.
y=2 Divide each side by 14.

10. 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).

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

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

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

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

15. Assignment: P. 439 3-12
Make sure you have work on your paper to
support your answer!! Put answer in an
ordered pair (x, y) with parenthesis.
Check to see if the ordered pair satisfies
both equations!!