Module 7 System of Equations Review

When eliminating, what is the first step?
-3x + 5y = 27
-3x + 2y = 9

• cross out the x's

• cross out the y's

• multiply either equation by -1

• multiply the top equation by 3

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

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

Solve the system of equations.

-4x - y = 1

3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• (-3, 11)

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

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