1. Solving System of Linear Equations
Elimination Method

2. Warm-up: solve the linear system by Elimination
y - 2x = -3
y - x = -1
(2,1)

3. Multiplying one equation
(5) ( )
-2x - 5y = 22
10x + 3y = 22
-2x - 5y = 22
-2x - 5y = 22
-2x - 5(-6) = 22
-2x = 22
-10x - 25y = 110
10x + 3y = 22
- 30
-2x = -8
y = 132 -2
x = 4
- 22y = 132
-22
y = -6
(4, -6)

4. Your turn! (-6, 7) x = -6 y = 7 4x + 2y = -10 -2x + 3y = 33
(2) ( )
4x + 2(7) = -10
4x = -10
4x + 2y = -10
-4x + 6y = 66
- 14
4x = -24
y = 56 4
x = -6
8y = 56 8
y = 7
(-6, 7)

5. 4x y = 70
Your turn… again!
4x y = 70
-4x y = -50
-2(2x - 5y = 25)
2x - 5y = 25
4x y = 70
4x y = 70
-4x y = -50
4x (1) = 70
4x = 70
20y = 20
-10 = -10
20 = 20
4x = 20 4
y = 1
x = 5
Answer: (5,1)

6. Hint: multiply the first equation by 4
Practice!
Hint: multiply the first equation by 4
2x - y = 9
3x + 4y = -14
Answer: ( 2, -5 )

7. Multiplying two equations
(5) ( )
3x + 5y = 10
5x + 7y = 10
3x + 5y = 10
3x + 5y = 10
(-3) ( )
3x + 5(5) = 10
3x = 10
15x + 25y = 50
-15x - 21y = -30
- 25
3x = -15
y = 20 3
x = -5
4y = 20 4
y = 5
(5, -5)

8. Your Turn! (7, 5) x = 5 y = 7 (3) ( ) 2x - 3y = -11 3x + 2y = 29
(-2) ( )
2x - 3(7) = -11
2x - 21 = -11
6x - 9y = -33
-6x -4y = -58
+ 21
+21
2x = 10
y = -91 2 10
x = 5
-13y = -91
-13
y = 7
(7, 5)

9. Summary: On Solving Linear Systems (Graphing, Substitution, Elimination Methods)
y = ½x + 1
y = -⅔x
y = 2x - 3
y = -3x + 2
y = -½x + 1
y = -5x -1
1.)
2.)
3.)
Substitution
2x + y = 8
y = x - 7
y = 3x - 6
-3x + y = -6
y = x + 4
y = 3x
1.)
2.)
3.)
Elimination
x + 2y = 7
3x - 2y = 1
8x - 9y = 19
4x + y = -7
4x - 3y = 11
3x - 5y = -11
1.)
2.)
3.)

10. Classwork 1.) 2.) 8x + 11y = 20 5x - 11y = -59 2x - 3y = 61
3.)
4.)
2x - 3y = 5
x + 2y = -1
20x + 3y = 20
-20x + 5y = 60