1. Solving Systems of Equations by Elimination2
Name: Pd
Algebra

2. { { { Three ways to solve a system of equations:
y = 2/5x – y = -3x + 15
Graphing {
4x – 3y = y = -3x + 15
Substitution {
5x + 3y = x – y = 6
Elimination

3. { 5x + 2y = -16 Ex1: Solve the system by using elimination.
Add systems +
– 5x
– 15y
= -75
-13y
= -91
-13
-13 {
y = 7
5x + 2y = x + 3y = 15
-5( )
1x + 3y = 15
Substitute the y
1x + 3(7) = 15
1x = 15
-21
-21 1x
= -6 1 1
x = -6
Solution (-6, 7)

4. { 6x + 3y = 9 Ex2: Solve the system by using elimination. Add systems
= 10 10 10 {
3( )
x = 1
2x + y = 3
4x – 3y = 1
2x + 1y = 3
Substitute the x
2(1) + 1y = 3
2 + 1y = 3 -2 -2 1y
= 1 1 1
y = 1
Solution (1, 1)

5. { -6x – 12y = -60 Ex3: Solve the system by using elimination.
Add systems +
-5x + 12y = 82
-11x
= 22
-11
-11 {
x = -2
3( )
-2x – 4y = -20
-5x + 12y = 82
-5x + 12 y = 82
Substitute the x
-5(-2) + 12y = 82
y = 82
-10
-10
12y
= 72 12 12
y = 6
Solution (-2, 6)

6. { 15x + 5y = 10 Ex4: Solve the system by using elimination.
Add systems +
-15x
– 9y
= -18
-4y
= -8 -4 -4 {
y = 2
15x + 5y = 10
5x + 3y = 6
-3( )
5x + 3y = 6
Substitute the x
5x + 3(2) = 6
5x + 6 = 6 -6 -6 5x
= 0 5 5
x = 0
Solution (0, 2)

7. { 8x – 10y = 6 Ex5: Solve the system by using elimination. Add systems+
15x
+ 10y
= -75
23x
= -69 23 23 {
2( )
x = -3
4x – 5y = x + 2y = -15
5( )
3x + 2y = -15
Substitute the x
3(-3) + 2y = -15
-9 + 2y = -15 +9 +9 2y
= -6 2 2
y = -3
Solution (-3, -3)

8. { 16x + 12y = 76 Ex6: Solve the system by using elimination.
= 76
Ex6: Solve the system by using elimination.
Add systems + 9x
– 12y
= 24
25x
= 100 25 25 {
4( )
x = 4
4x + 3y = x – 4y = 8
3( )
4x + 3y = 19
Substitute the x
4(4) + 3y = 19
16 + 3y = 19
-16
-16 3y
= -3 3 3
y = -1
Solution (4, -1)

9. { 15x + 25y = -55 Ex7: Solve the system by using elimination.
= -55
Ex7: Solve the system by using elimination.
Add systems +
-15x
– 6y
= 93
19x
= 38 19 19 {
5( )
y = 2
3x + 5y = x + 2y = -31
3x + 5y = -11
-3( )
Substitute the x
3x + 5(2) = -11
3x = -11
-10
-10 3x
= -21 3 3
x = -7
Solution (-7, 2)

10. { -20x – 15y = 10 Ex8: Solve the system by using elimination.
= 10
Ex8: Solve the system by using elimination.
Add systems +
20x
+ 8y
= -52
-7x
= -42 -7 -7 {
y = 6
5( )
-4x – 3y = x – 2y = 13
-4x – 3y = 2
-4( )
Substitute the x
-4x – 3(6) = 2
-4x – 18 = 2
+18
+18
-4x
= 20 -4 -4
x = -5
Solution (-5, 6)

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