1. Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will study vocabulary words.

2. 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

3. Daily Homework Quiz For use after Lesson 7.1 Solve the linear system by graphing. 2x + y = –3 –6x + 3y = 3 ANSWER (–1, –1)

6. 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

7. 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

8. 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

9. 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

10. EXAMPLE 2 Use the substitution method Solve the linear system : x – 2y = –6 Equation 1 4x + 6y = 4 Equation 2 SOLUTION Solve Equation 1 for x. x – 2y = –6 Write original Equation 1. x = 2y – 6 Revised Equation 1 STEP 1

11. 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 property 8y – 24 + 6y = 4 14y – 24 = 4 Simplify. 14y = 28 Add 24 to each side. y = 2 Divide each side by 14. STEP 2

12. 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

13. 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

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

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

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