Solve Linear Systems by Substitution

•Students will solve systems of linear equations by substitution.

•Students will do assigned homework.

•Students will study vocabulary words.

Lesson 7.2, For use with pages 435-441

Solve the equation.

1. 6a – 3 + 2a = 13

2. 4(n + 2) – n = 11

ANSWER a = 2

ANSWER n = 1

Daily Homework Quiz For use after Lesson 7.1

Solve the linear system by graphing.

2x + y = –3 –6x + 3y = 3

ANSWER (–1, –1)

EXAMPLE 1 Use the substitution method

Solve the linear system:

y = 3x + 2

Equation 2

Equation 1

x + 2y = 11

Solve for y. Equation 1 is already solved for y.

SOLUTION

STEP 1

EXAMPLE 1 Use the substitution method

7x + 4 = 11 Simplify.

7x = 7 Subtract 4 from each side.

x = 1 Divide each side by 7.

Substitute 3x + 2 for y.x + 2(3x + 2) = 11

Write Equation 2.x + 2y = 11

Substitute 3x + 2 for y in Equation 2 and solve for x.

STEP 2

EXAMPLE 1 Use the substitution method

ANSWER

The solution is (1, 5).

Substitute 1 for x in the original Equation 1 to find the value of y.

y = 3x + 2 = 3(1) + 2 = 3 + 2 = 5

STEP 3

GUIDED PRACTICE

CHECK

y = 3x + 2

5 = 3(1) + 2?

5 = 5

Substitute 1 for x and 5 for y in each of the original equations.

x + 2y = 11

1 + 2 (5) = 11?

11 = 11

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 2SOLUTION

Solve Equation 1 for x.

x – 2y = –6 Write original Equation 1.

x = 2y – 6 Revised Equation 1

STEP 1

EXAMPLE 2 Use the substitution method

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.

Distributive property8y – 24 + 6y = 4

14y – 24 = 4 Simplify.

14y = 28 Add 24 to each side.

y = 2 Divide each side by 14.

STEP 2

EXAMPLE 2 Use the substitution method

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).

STEP 3

4(–2) + 6 (2) = 4 ?

GUIDED PRACTICE

CHECK

–2 – 2(2) = –6?

–6 = –6

Substitute –2 for x and 2 for y in each of the original equations.

4x + 6y = 4

4 = 4

Equation 1 Equation 2

x – 2y = –6

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 (1, 7)

EXAMPLE 2 Use the substitution method

x + 2y = –6

GUIDED PRACTICE for Examples 1 and 2

x – y = 32.

ANSWER (0, –3)

Solve the linear system using the substitution method.

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 (–2, –1)