1. Solve System by Linear Combination / Addition Method
Objectives:
To solve a system of equations using the Linear Combination Method

2. Example 1 (5,-2) Solve using the addition method. x – y = 7 x + y = 3

3. Example 2 (4,1) Solve using the addition method. 2x + 3y = 11

4. Practice
Solve using the addition method. 1) 2)

5. Example 3 Solve using the addition method. 3x – y = 8 x + 2y = 5
write in standard form
(-3)
( ) ( )
x + 2y = 5
(-3)
multiply as needed
3x – y = 8
-3x – 6y = -15
addition property
-7y = -7
3x - (1) = 8
y = 1
3x = 9
x = 3
(3,1)

6. Example 4 Solve using the addition method. 8x + 2y = -10
write in standard form
(-2)
( ) ( )
4x – 3y = 15
(-2)
multiply as needed
8x + 2y = -10
addition property
-8x + 6y = -30
8y = -40
8x + 2(-5) = -10
8x - 10 = -10
y = -5
8x = 0
x = 0
(0,-5)

7. Practice
Solve using the addition method. 1) 2)