Systems of equations and inequalities Review

Solving Systems Pt. 1

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)

Solving Systems Pt.2

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

Solving Systems Pt. 3

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? 

Hint: What mathematical symbol(s) are used?

> 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

2(2-2v)>-10+3v

v<2

500

Jake plans to board his dog while he is away on vacation. Boarding house A charges $90 plus $5 per day. Boarding house B charges $100 plus $4 per day. For how many days must Jake board his dog for A to be less expensive than B?

d<10, Less than 10 days

Miscellaneous

100

This 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

-2(3+4n)-3<11+2n

n>-2

500

The Student Council decides to raise money by organizing a dance. Tickets are $7.50 each, but the cost of hiring the video-DJ is $1200. How many tickets must be sold to make a profit of more than $1500?

T>360