1. The Substitution Method Objectives: To solve a system of equations by substituting for a variable

2. Example 1 Solve using substitution. y = 3x 2x + 4y = 28 2x + 4(3x) = 28 2x + 12x = 28 14x = 28 x = 2 y = 3(2) y = 6 (2,6) y = 3x

3. Practice Solve using substitution. 1)x + y = 5 x = y + 1 2) a – b = 4 b = 2 – 5a

4. Example 2 Solve using substitution. 2x + y = 134x – 3y = 11 y = -2x + 134x – 3(-2x + 13) = 11 4x + 6x – 39 = 11 10x – 39 = 11 10x = 50 x = 5 2x + y = 13 2(5) + y = 13 10 + y = 13 y = 3 (5,3)

5. Practice Solve using substitution. 1)x – 2y = 8 2x + y = 8 2) 3x + 4y = 2 2x – y = 5

6. Example 3 Solve using substitution. The sum of a number and twice another number is 13. The first number is 4 larger than the second number. What are the numbers? Let x = the first number Let y = the second number x + 2y = 13 x = y + 4 y + 4 + 2y = 13 3y + 4 = 13 3y = 9 y = 3 x = y + 4 x = 3 + 4 x = 7

7. Practice Translate to a system of equations and solve. 1) The sum of two numbers is 84. One number is three times the other. Find the numbers.