Systems of Equations

Graphing

100

y=-5/3x+3

y=1/3x-3

(3,-2)

200

y=4x+3

y=-x-2

(-1,-1)

300

y=-1/2x-1

y=1/4x-4

(4,-3)

400

y=3x-4

y=-1/2x+3

(2,2)

500

y=-1/2x-2

y=-3/2x+2

(4,-4)

Set Up Substitution

100

Solve an equation for one variable, and substitute it into the other equation (DO NOT SOLVE):

-5x+y=-2

-3x+6y=-12

-3x+6(5x-2)=-12

200

Solve an equation for one variable, and substitute it into the other equation (DO NOT SOLVE):

x+4y=24

x-5y=-10

(24-4y)-5y=-10

or

(-10+5y)+4y=24

300

Solve an equation for one variable, and substitute it into the other equation (DO NOT SOLVE):

4x+2y=10

x+3y=10

4(10-3y)+2y=10

400

Solve an equation for one variable, and substitute it into the other equation (DO NOT SOLVE):

4x+2y=-12

3x+y=-10

4x+2(-10-3x)=-12

500

Solve an equation for one variable, and substitute it into the other equation (DO NOT SOLVE):

-2x+y=-11

4x+4y=4

4x+4(-11+2x)=4

Substitution

100

-3x-5y=6

y=-3

(3,-3)

200

y=6x-14

y=-8x

(1,-8)

300

8x+3y=-9

6x=-18

(-3,5)

400

y=6x-11

-2x-3y=-7

(2,1)

500

-4x+y=6

-5x-y=21

(-3,-6)

Set up Elimination

100

Which equation will you multiply and what number will you use?

3x+4y=12

2x-2y=10

Bottom by 2

200

Which equation will you multiply and what number will you use?

6x-7y=20

5x-14y=5

Top by -2

300

Which equation will you multiply and what number will you use?

x+5y=2

8x-7y=3

Top by -8

400

Which equation will you multiply and what number will you use?

6x-10y=0

8x+30y=0

Top by 3

500

There are 2 different options to set this system up to use elimination. What are the 2 options?

-x+3y=7

-2x-y=10

Top by -2

Bottom by 3

Elimination

100

x+y=7

x-y=3

(5,2)

200

2x-3y=16

2x+3y=4

(5,-2)

300

6x-2y=4

4x-2y=2

(1,1)

400

3x-10y=-25

4x+40y=20

(-5,1)

500

-3x+2y=17

x-5y=-10

(-5,1)