Systems of equations and inequalities Review

Graphing

100

y = 2x + 2

y = x - 1

(-3, -4)

200

y = 2x + 4

y = 3x + 2

(2, 8)

300

x = 3

y = 2x + 1

(3, 7)

400

4x + 2y = 8

2x + y = 4

No solution

500

y = 1/2 x + 2

y = 1/4 x + 4

(8, 6)

Substitution

100

y = 2

3x + 2y = 10

(2, 2)

200

x + 3y = 2

-x + 2y = 3

(-1, 1)

300

x - 2y = -10

3x - y = 0

(2, 6)

400

2x – 3y = –2

 4x + y = 24

(5, 4)

500

5x - y = -13

-5x +2y = 24

no solution

Elimination

100

x + 3y = 5

2x -3y = -8

(-1, 2)

200

-5y + 8x = -18

5y + 2x = 58

(4, 10)

300

3y - 5x = -26

-2y - 5x = -16

(4, -2)

400

3x−4y=8

18x−5y=10

(0, -2)

500

4x−9y−2=0

12x−5y+38=0

(-4, -2)

Linear Inequalities

100

What does a dotted line mean when graphing linear inequalities?

> or <

200

How is graphing systems of inequalities different than graphing systems of equations? (2 things)

Sometimes they use dotted lines and you have to shade for inequalities.

300

How do you know where to shade when solving systems of inequalities?

Test a point in the equations. If it's true, shade toward the point. If false, shade away. Where the shaded regions overlap is your solution.

400

y≤x−2

y>−3x+5

Shaded toward the bottom right

500

2x – 3y < 12 

x + 5y < 20 

Darkly shaded top left corner