1. Solving Systems of Equations by Elimination Part 2

2. Solve the System of Equations
These need to have the same coefficient with opposite signs ( )
2x + y = 20
10x + 5y = 100
• (5) =
6x - 5y = 12
6x -5 y = 12
16x
+ 0y
= 112
16x = 112
6x - 5y = 12
x = 7
6(7) - 5y = 12
42 - 5y = 12
-5y = -30
y = 6
Solution (7, 6)

3.   Check 6x - 5y = 12 2x + y = 20 6(7) - 5(6) = 12 2(7) + 6 = 20
Solution (7, 6)
6x - 5y = 12
2x + y = 20
6(7) - 5(6) = 12
2(7) + 6 = 20
= 12
= 20
12 = 12 
20 = 20 

4. Solve the System of Equations
These need to have the same coefficient with opposite signs ( )
-5x + y = -3
-40x + 8y = -24
• (8) =
3x - 8y = 24
3x - 8 y = 24
-37x
+ 0y
= 0
-37x = 0
3x - 8y = 24
x = 0
3(0) - 8y = 24
0 - 8y = 24
-8y = 24
y = -3
Solution (0, -3)

5.   Check 3x - 8y = 24 -5x + y = -3 3(0) - 8(-3) = 24 -5(0) + -3 = -3
Solution (0, -3)
3x - 8y = 24
-5x + y = -3
3(0) - 8(-3) = 24
-5(0) + -3 = -3
= 24
= -3
24 = 24 
-3 = -3 

6. Solve the System of Equations
These need to have the same coefficient with opposite signs ( )
-7x - 8y = 9
-63x - 72y = 81
• (9) =
-4x + 9y = -22 ( )
-32x +72y = -176
•(8)=
-95x
+ 0y
= -95
-95x = -95
-4x + 9y = -22
x = 1
-4(1) + 9y = -22
-4 + 9y = -22
9y = -18
y = -2
Solution (1, -2)

7.   Check -4x + 9y = -22 -7x - 8y = 9 -4(1) + 9(-2) = -22
Solution (1, -2)
-4x + 9y = -22
-7x - 8y = 9
-4(1) + 9(-2) = -22
-7(1) - 8(-2) = 9
= -22
= 9
-22 = -22 
9 = 9 

8. Solve the System of Equations
These need to have the same coefficient with opposite signs ( )
3x - 2y = 2
-15x + 10y = -10
• (-5) = ( )
10x - 10y = 20
5x - 5y = 10
• (2) =
-5x
+ 0y
= 10
-5x = 10
3x - 2y = 2
x = -2
3(-2) - 2y = 2
-6 - 2y = 2
-2y = 8
y = -4
Solution (-2,-4)

9.   Check 5x - 5y = 10 3x - 2y = 2 5(-2) - 5(-4) = 10
Solution (-2, -4)
5x - 5y = 10
3x - 2y = 2
5(-2) - 5(-4) = 10
3(-2) - 2(-4) = 2
= 10
= 2
10 = 10 
2 = 2 