Solving Systems of Equations

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

2x - y = 0

4x - y = 0

• (1,2)

• (0,0)

• No Solutions

• Infinite Solutions

What is the solution?

• A

• B

• C

• D

The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

• x=8

• x=3

• x=11

• x=5

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120

• 3x+3y=134
  4x+3y=120

• 4x+3y=134
  3x+3y=120

• 7xy=134
  6xy=120

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions