Systems of Equations and Inequalities Test

A library contains 2000 books.

There are 3 times as many non-fiction books as fiction books.

Write and solve a system of inequalities to determine the number of non-fiction and fiction books.

• 750 non-fiction,

  250 fiction

• 1000 non-fiction,

  1000 fiction

• 1200 non-fiction,

  800 fiction

• 1500 non-fiction, 500 fiction

One number added to three times another number is 24.

Five times the first number added to three times the other number is 36.

Find the numbers.

• 3, 7

• 6, 6

• 12, 4

• 15, 9

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent.

• consistent and dependent

• consistent and independent

• inconsistent

Eight times a number plus five times another number is -13.

The sum of the two numbers is 1.

What are the numbers?

• -5, 6

• -6, 7

• -7, 8

• -8, 9

Which point is a solution to the system of inequalities?

• (-8,2)

• (-2,-5)

• (0,6)

• (4, 3)

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

Solve the system of inequalities by graphing.

• 
• 
• 
• 

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450