Systems of Equations Process Questions

What is the number of solutions to the system of equations? (Notice there are two lines graphed one on top of the other.)

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

To Find the solution to this system of equations, Juan decided to multiply the entire first equation by -1. What method is Juan employing to find the solution?

• Substitution

• Graphing

• No Solution

• Elimination

What is the first step Terri could take to find the solution to the system of equations using the Elimination Method?

• Multiply by -1 through one equation to flip the signs and create opposite y-values.

• Multiply by -1 through one equation to flip the signs and create opposite x-values.

• Multiply by 1 through one equation to flip the signs and create opposite y-values.

• Isolate a variable and substitute the value in the other equation.

Tauren graphed the two equations shown in the System of Equations. He discovered that the lines appeared in exactly the same location. What is the solution to this system of equations?

• (-7, -9)

• (-10, 5)

• No Solution

• Infinitely Many Solutions

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 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

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

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

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

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

AJ was asked to find the solution to this system of equations. x = 7 - 2y 2x + y = 5 Noticing that x was isolated and set equal to 7 - 2y, he decided to replace x in the second equation with its value. What method is AJ using and what equation did he write?

• Elimination; 2(7-2y) + y = 5

• Graphing; 2x = (7-2y) + y = 5

• Substitution; 2(7-2y) + y = 5

• Substitution; x = 7 - 2y + 2x + y = 5