Solving systems review!

Category 1

100

Is the following ordered pair a solution to the inequality? 

2x + y > 8 & (3,2)

2(3) + 2 > 8 

8 > 8

FALSE

200

Graph the inequality:

x + 4y < 12

dashed

y < -1/4x + 3

Shade below inequality 

300

Solve the system using substitution:

-x – y = -1

3x + 3y = 3

Infinite many solutions

400

Solve the system using matrices:

3x – 4y = 1

-5x + 2y = 3

(-1,-1)

Category 2

100

Is the following ordered pair a solution to the system of inequalities? 

3x - y < 10  & (1,1)

2x + y ≥ 3

3(1)-1<10                           2(1)+1≥3

2<10                                     3≥3

TRUE                                     TRUE

200

Graph the inequality:

3x – 2y < 6

dashed line

y > 3/2x - 3

Shade above inequality 

300

Solve the system using elimination:

-5x + 5y = 10

-2x + 2y = -4

Infinite many solutions

400

Solve the system using matrices:

2x + 2y = 0

4x – y = -20

(4,-4)

Category 3

100

Which of the ordered pairs that are solutions to the inequality shown in the graph:

(4, -6)   (3, -3)   (-3, -3)   (-5, 1)      (0, 0)   

(4,-6)

(-3,-3)

(-5,1)

200

Graph the system of inequalities 

x+2y > 14

3x - y > 4

INTERSECTION: Top right corner

300

Solve the system by graphing:

4x + y = 2

2x – 2y = 6

(1,-2)

400

Solve the system using matrices:

-5x + 5y = 25

-2x – 4y = 16

(-6,-1)

Category 4

100

Transform the linear equation into standard form:

y = 2x - 4

2x – y = 4

200

Write the system of inequalities from the graph

y ≥  1/3 x+3 

y >  -4/3 x -2

300

Is the following ordered pair a solution to the inequality:

2x + y > 8   &  (3,7)

2(3) + 7 > 8

13 > 8

TRUE STATEMENT

400

Orbitz is offering a special for a hotel in Mexico.  There are two options:  4 nights and 2 meals for $400 or 3 nights and 3 meals for $345.  How much is it per night and per meal?

Night: $85

Meal: $30

Category 5

100

Find the x-and y-intercepts for the following linear equation:

3x – 2y = 24

(8,0) and (0,-12)

200

Transform the linear equation into standard form:

y = - 3/5 x+1

3x + 5y = 5

300

Find the x and y intercepts for the equation:

15x – 10y = 100

(20/3, 0) and (0,-10)

400

Natalie is checking items being shipped to the school bookstore.  The shipment contains notebooks that cost $22 per box and mugs that cost $40 per box.  She counts 16 boxes, and the invoice states that the order totals $460.  How many boxes of each item were received?

10 notebooks

6 mugs