Systems of Equation Special Cases

Solve the system and determine the number of solutions it has. If it has one solution, name it.
-6x+y=6
-3x+y=6

• No Solution

• Infinitely Many Solutions

• One Solution; (-1,0)

• One Solution; (0,6)

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

• intersecting lines

• parallel lines

• skew lines

• same lines

If a system of equations has infinitely many solutions, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• same lines

If a system of equations has infinitely many solutions, what do you know about the slopes and y-intercepts of the two equations?

• They have different slopes and different y-intercepts.

• They have the same slopes and different y-intercepts.

• They have the same slopes and the same y-intercepts.

• They have different slopes and the same y-intercepts.

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

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

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

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

Which two lines show a system with no solution?

• Purple and Green

• Green and Red

• Purple and Blue

• Red and Blue

If a system of equations has no solution, what do you know about the slopes and y-intercepts of the two equations?

• They have different slopes and different y-intercepts.

• They have the same slopes and different y-intercepts.

• They have the same slopes and the same y-intercepts.

• They have different slopes and the same y-intercepts.