Introducing Systems of Equations

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

Find the solution to the system.
y = x-6
y = -3x + 2

• (0, -6)

• (6, 0)

• (-4, 2)

• (2, -4)

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

The ordered pair that satisfies all equations in the system.

• system of equations

• function

• graph

• solution of a system

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1.5)

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 8)

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

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

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions