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

Vocab

100

Consists of two or more linear equations in the same variables.

System of linear equations (linear system)

200

The method of solving equations where you add or subtract equations to end up with one variable.

Elimination

300

How can you tell if a linear system has infinitely many solutions?

The equations are the same or solving the system provides a true statement with no variables.

400

A linear system with no solution, when the graphs of the equations are parallel

Inconsistent system

500

A linear system with infinitely many solutions, when the graphs of the equations are the same

Consistent dependent system

Don't say 10!

100

This is the sum of 7 and 3

(5 x 2)

200

What is the solution to the system x = 10, y=10?

(x, x)

300

This is the product of 55 and 2

100+5+5

400

Wimbeldon and The French Open are championships associated wtih this sport

(5+5)nis

500

This is the solution to the system  x + y = 9 and x - y = 9

What is (0, 9)