Graphing 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

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines

• the same line 

• Intersecting lines

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

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

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

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.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes

• 90 minutes
  2x + 4y = 315

• 60 minutes
  3x + 4y = 450

• 30 minutes

How many solutions does this system have?

y = 2x + 1

y = 4x - 1

• One Solution

• No Solution

• Infinite Solutions

How many solutions does this system have?

y=2x + 4

y=2x -4

• One Solution

• No Solution

• Infinite Solutions

7x+4y =12 
x + 2y = -4

• (-4,4)

• (4,4)

• (4,-4)

• (-4,-4)