Systems of Equations and Linear Inequalities

Which system of linear inequalities is shown in the graph?

Graph the system.

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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

Solve the following equations for x and y:
-6x+6y=6
6x-3y=12

• (6, 5)

• (5, 6)

• (4, 4)

• (2, 4)

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

• (3,-9)

• (-3,-9)

• (-3,9)

• (0,1)

Solve the system of Equation (x,y)
–2x + y = 10
4x – y = –14  

• (1,5)

• (6,2)

• (-2,6)

• (4,6)

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

• (2,2)

• (-2, -2)

• (-2,2)

• (2,1)

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Solve the following system of equations:
2x+3y=17
y=4x+1

• (-1,-3)

• (1,5)

• (1,3)

• (2,4)