1. Systems of Equations
Solve by Graphing

2. Graph both linear equations on the same graph
y = x – 2 y x x y 1 2 -2 -1
y = -2x + 1
Solution
(1,-1) x y 1 2
(1, -1) 1 -1 -3

3. Graph both linear equations on the same graph
y = 4x + 3 y x x y -1 -2 3 -1 -5
y = -x - 2
(-1,-1)
Solution x y 1 2
(1, -1) -2 -3 -4

4. Systems of Equations
Solve by Substitution

5. x + 3y = 20 x = 4 + 5y
x = 4 +5y
x = 4 +5(2)
x = 4 +10
4 + 5y + 3y = 20
8y + 4 = 20
x = 14
8y = 16
Solution (14,2)
y = 2

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

7. Systems of Equations
Solve by Elimination

8. Solve the System of Equations
2x + 4y = 40
2x + 4y = 40
-2x - y = -16
2x + 4(8) = 40
2x + 32 = 40 0x
+ 3y
= 24
2x = 8
3y = 24
y = 8
x = 4
Solution (4, 8)

9. Solve the System of Equations
These need to have the same coefficient [ ]
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)