Solving Systems of Equations

One, None, Infinite

100

y = - 3x + 7

y = - 3x - 18

No Solution

200

y = 1/3x + 4

y = 5x - 2

One Solution

300

y = 5x - 3

y = 5x + 2 - 5

Infinite Solutions

400

y = 3x + x - 6

y = 4x + 5

No Solution

500

3y = 12x

y = 4x

Infinite Solutions

One-Step

100

x + 10 = 17

x = 7

200

x - 9 = 13

x = 22

300

7x = 42

x = 6

400

9x = 72

x = 8

500

x/15 = 3

x = 45

Two-Step

100

2x + 4 = 18

x = 7

200

8x - 13 = 11

x = 3

300

3x + 10 = 5x

x = 5

400

4x + 2 = x + 29

x = 9

500

6x - 16 = 4x + 24

x = 20

Setting Equal

100

y = 5x + 3

y = x + 7

( 1 , 8 )

200

y = x + 10

y = 4x + 1

( 3 , 13 )

300

y = 2x + 11

y = 4x + 1 

( 5 , 21 )

400

y = - 2x + 21

y = 3x + 1

( 4 , 13 )

500

y = - x + 9

y = 1/2x

( 6 , 3 )

Distribution/Substitution

100

3( x - 3 ) = 6

x = 5

200

2(x + 10 ) = 3x

x = 20

300

5( x - 2 ) = 4x + 3

x = 13

400

y = 2x

2x + 2y = 30

( 5 , 10 )

500

1/2 y = 10

y = x + 4

( 16 , 20 )