Classify a System of Equations

Without graphing, classify each system as independent, dependent, or inconsistent.
-3x + y = 4
3x - y = 1

• Independent

• Dependent

• Inconsistent

Without graphing, classify each system as independent, dependent, or inconsistent.
x - 3y = 2
4x - 12y = 8

• Independent

• Dependent

• Inconsistent

Solve the system by substitution.
y = 2x - 1
3x - y = -1

• Infinite Solutions

• (-5, -2)

• (-2, -5)

• No solution

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two 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

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

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• 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 $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