graphing systems of equations
Substitution
elimination (addition and subtraction)
Elimination (multiplication)
systems of inequalities
100

y=2x+1

y=x+4

(1,3)

100
y=3x+2

x+y=11

x=1.8 y=7.4

-7(1.8, 7.4)

100

3x+2y=16

-3x+y=5

y=7

x=2/3

100

2x+3y=12

4x-y=2

y=22/7

x=9/7

(9/7, 22/7)

100

y<x+2
y>x-1

between lines

200

y=-2x+5

y=-2x-3

no solution 

200

y-4

2x+y=10

y=6 x=2

(2,6)

200
x+2y=10

-x+3y=5

y=3

x=4

(4,3)

200

3x-2y=1

5x+3y=16

x=35/19

y=43/19

200

y>=2x-3

y<-x+4

Region overlaps 

300

Y=0.5x+2

x-2y=-4

x-2y=-4-7

y=6.5x+2

infinite solutions 

300
y=-2x+5

4x+y=1

x=1, y=3-7

(1,3)

300

2x+y=9

4x-y=3

x=2

y=5

(2,5)

300

x+4y=10

3x-2y=-2

y=16/7

x=6/7

300
Y<=-2x+6

y>=x-2

close area between the two lines

400

-y=x-1

y=2x+5

(2,1)

400

x=0.5

3x+y=6

y=-4, x=-2

-7(2,-4)

400

5x-2y=4

-5x-y=-1

y=-1

x=0.4

(0.4,1)

400

4x+5y=11

6x-10y=-2

x=10/7

y=37/35

(10/7, 37/35)

400
y>3x-1

y<3x+2

region between the two dashed lines equations have same slope 

500
y=3x+2

y=3x-4

no solution lines don't intersect
500

y=2x+1

3x+y=10

x=1.8

y=4.6

(1.8, 4.6)

500

6x+5y=7

-2x+5y=1

x=0.75

y=0.5

(0.75, 0.5)

500

2x+y=5

3x-2y=4

x=2

y=1

(2,1)

500

y<=1

x>-2

region below or on the horizontal line

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