Systems of Equations

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

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

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

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)
• (5, 1)
• (0.25, 2)
• ∅

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 

• (5, 8)
• (5, -8)
• (-5, -18)
• (-5, 8)

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

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 

• y = 9.65 + x
  y = 8.40 + x
• y = 9.65x + 43
  y = 8.40x + 58
• y =9.65x
  y = 8.40x
• y = 9.65x - 43
  y = 8.40x - 58

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

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

What is the number of solutions to the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions