Systems of Equations

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?

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

Solve the system of equations algebraically (by substitution.)
y = x
y = 2x - 4

• (2, 4)
• (4, 4)
• (-2, -4)
• (-4, -4)

Solve the system of equations algebraically (by substitution.)
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

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

Find  f(7)  if
f(x) = 3x - 1

• 31
• 7
• 20
• 1

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

Parallel Lines never intersect because...

• They have the same slopes and different y-intercepts. 
• They have the same y-intercept.
• They have negative reciprocal slopes.
• They have no y-intercepts. 

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

Tags

CCSS.HSA.CED.A.3