Solving Systems of Equations

Substitution Basics

100

3u + z = 15 u = 4

z = 2 3(4) + 2 = 15

200

y = 6x - 11 y = 7

x = 3 7 = 6(3) - 11

300

4x - 3y = 18 x = 6

y = 2 4(6) - 3(2) = 18

400

y = 5x - 7 y =

x = 7 28= 5(7) - 7

500

-5x + y = -3 x = -5

y = 22 -5(5) + 22 = -3

Substitution

100

y = 6x - 11 -2x - 3y = -7

1 = 6(2) - 11 -2(1) - 3(2) = -7 (2,1) (x,y)

200

2x - 3y = -1 y = x -1

2(4) - 3(3) = -1 3 = 4 - 1 (4,3) (x,y)

300

y = -3x + 5 5x - 4y = -3

2 = -3(1) + 5 5(1) - 4(2) = -3 (1,2) (x,y)

400

-3x - 3y = 3 y = -5x - 17

-3(-4) - 3(3) = 3 3 = -5(-4) - 17

500

y = -2 4x - 3y = 18

4(-2) - 3(3) = 18 (-2,3) (x,y)

EliminationBasics

100

-4x-2y=-12 4x+8y=-24

-4(6) - 2(-6) = -12 4(6) + 8(-6) = -24 (6,-6) (x,y)

200

4x + 8y = 20 -4x + 2y = -30

x=7 y= -1

300

-6x + 5y = 1 6x + 4y = -10

x=-1 y= -1

400

-3x - 4y = 2 3x + 3y = -3

x= -2 y= 1

500

-6x + 6y = 6 -6x + 3y = -12

x=5 y=6

Elimination

100

8x + y = -16 -3x + y = -5

x= -1 y=-8

200

7x + 2y = 24 8x + 2y = 30

x = 6 y = -9

300

5x + y = 9 10x - 7y = -18

x = 1 y = 4

400

-4x + 9y = 9 x - 3y = -6

x=9 y=5

500

-7x + y = -19 -2x + 3y = -19

x = 2 y = -5