1. 4 minutes
Warm-Up
1) Determine whether (-1,7) is a solution of the system.
3x – y = -10
-x + y = 8
2) Solve for x where 5x + 3(2x – 1) = 5.

2. 5.2 The Substitution Method
Objectives:
To solve a system of equations by substituting for a variable

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

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

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

6. Practice Solve using substitution. x – 2y = 8 2) y = 3x 2x + y = 8

7. 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
y y = 13
x = y + 4
3y + 4 = 13
3y = 9
y = 3
x = y + 4
x = 3 + 4
x = 7

8. 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.