Systems of equations and Inequalities

Systems of equations and Inequalities

Multiple Choice

Match: the overlap is on the left!

• y ≤ 3x   and  y ≤ -2x + 4
• y > 3x   and  y > -2x + 4
• y < 3x   and  y > -2x + 4
• y > 3x   and  y < -2x + 4

Multiple Choice

There are 50 donkeys and chickens on a farm.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50
• d + c = 50
  4d + 2c = 174
• d + c = 50
  2d + 4c = 174
• d + c = 174
  2d + 4c = 50

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Multiple Choice

Westlake Catalog sells mavericks jerseys for $39 and Rangers hats for $18. Megan orders "j" jerseys and "h" hats. The total numbers of items ordered is 25, and the total cost is $702. Which system of equations represent this situation?

• j = 39

  
  

  h = 18

• j + h = 25

  
  

  j + h = 702

• j + h = 25

  
  

  39j + 18h = 702

• j + h = 702

  
  

  39j + 18h = 25

Multiple Choice

A radio station is giving away tickets to a concert. There are $10 tickets and $20 tickets. They want to give away at least 20 tickets but want to spend at most $280.

Let x = the number of $10 tickets

Let y = the number of $20 tickets

Which system of inequalities models the situation?

• x + y $\ge$ 20
  10x + 20y $\le$ 280

• x - y $\ge$ 20
  20x + 10y $\le$ 280
  

• x + y $\ge$ 280
  10x + 20y $\le$ 20

• x + y $<$ 20
  10x + 20y $>$ 280

Multiple Choice

What type of solution does this system have?
2y - 30x = -6
-3y + 45x = 15

• One solution
• No solution
• Infinite solutions

Multiple Choice

What type of solution does the system below have?
8x - 4y = 12
y = 2x - 3

• One solution
• No solution
• Infinite solutions

Multiple Choice

An exam worth 145 points contains 50 questions.  Some questions are worth two points and some are worth five points.  How many five point questions are on the test?

• 20
• 35
• 15
• 25

Multiple Choice

Which points are solutions to the system shown?

• (5, 3) (6, -3)
• (3, 3) (5, -3)
• (-2, 2) (-4, 4)
• (1, 2) (1, 5)

Multiple Choice

What are the two linear inequalities graphed here?

• y ≤ - x + 4
   y < x - 2
• y ≤ - x + 4
   y > x - 2 
• y ≤ - 2x + 4
   y > 2x - 2
• y ≤ - x + 2
   y > x - 4