Solving Systems Using Equal Values

Which is the best method for solving this system of equations?

y=3x + 7

y=3x -2

• Elimination

• Substitution

• Graphing, Not Graphing...

  (aka Picturing the Graph)

  (aka Using graphing skills but not actually graphing)

To solve a system by Equal Values, set both __________ to each other. Solve the equation for __________ variable. Substitute the value you got back into one of the original equations to solve for the second variable. List your solution as a __________ (x, y).

• two

• equations

• coordinate pair

• one

• variables

Solve for y.

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

• Infinite Number of Solutions

• No Solution

• One Solution

• Two Solutions

• Not possible

There are a total of 15 horses and chickens in a barn. Altogether, there are 44 legs.  

Which system of equations represents the number of horses(x) and the number of chickens(y) in the barn?

• x + y = 15
  4x + 2y = 44

• 4x + 2y = 15
  x + y = 44

• x = 2y + 44
  4x = y + 15

• 2x - 4y = 44
  x - y = 15

Solve the system of equations.

• (10, 3)

• (6, 3)

• (15, 3)

• No solution

• Infinite Solution

The solution is:

• (4, 3)

• (3, 4)

• (-4, 3)

• No solution

A __________ is a set of two or more equations. A system of equations means finding the __________ where the two lines intersect, or the one solution (x, y) that makes both equations true. There are three ways to solve: substitution, elimination, and equal values.

• System of Equations

• solving

• coordinate pair

• slope

• Slope-Intercept From (y=mx+b)

This system has an infinite number of solutions, TRUE or FALSE?

• TRUE

• FALSE