Solving Systems by Elimination

One Variable

100

x - 2 = 8

x + 2 = 12

x = 10

200

2y - 12 = -6

y + 12 = 15

y = 3

300

19p - 8.2 = 67.8

-8p + 8.2 = -23.8

p = 4

400

43n + 100 = -115

-15n - 100 = -25

n = -5

500

17s + 45 = -21.3

17s - 45 = -111.3

s = -3.9

Two Variables

100

x + y = 13

x - y = 7

(10, 3)

200

2y - x = -2

3y + x = 27

(12, 5)

300

2x + 4y = 68

-2x + 3y = 9

(12, 11)

400

-6x+5y=1

6x+4y=-10

(-1, -1) 

500

20x+40y=500

-20x+60y=400

(7, 9) 

Substitution

100

y=2x+4

x=1

(1, 6) 

200

2x+y=12

y=4x

(2, 8) 

300

x= 4y

x-4y=0

Infinite Solutions 

400

y=-2x+8

y=x+2

(2, 4) 

500

y=-2x-1

y=-4x-5

(-2, 3)