Systems of Linear Equation Pairs

two or more linear equations with the same variables

• piecewise defined function

• linear inequality

• solution to a linear inequality

• boundary line

• system of linear equations

A method to solve a system. One equation is solved for one of the variables then the expression for that variable is substituted into the other equation

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

A method to solve a system. Two equations are combined to eliminate one variable.

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

Lines that occupy the same location, pass through the same set of ordered pairs and intersect infinitely many times.

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4

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

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