Solve Systems of Equations All Methods

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

• Parallel lines

• the same line 

• Intersecting lines

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Solve the system of equations by substitution:

y = 4x+1

3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

a method to solving a system of equations by getting rid of one of the variables first to solve for the other variable. 

• Systems by Graphing

• Systems by Substitution

• Systems by Elimination

• Systems by Drawing

a method of solving a system of equations by taking a variable out and replacing it with an expression.

• Systems by Graphing

• Systems by Substitution

• Systems by Elimination

• Systems by Drawing

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

• (3,-9)

• (-3,-9)

• (-3,9)

• (0,1)

Solve the system by substitution.

−x + 5y = 12

y = −2x − 2

• (−2, −7)

• (−2, 2)

• (−2, −2)

• (2, −2)

Solve the system by elimination.

7x - y = -10

-7x + 5y = -6

• (-2, -4)

• (-2, -1)

• (-4, -1)

• (6, -8)

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

What is the solution to this system of equations? Solve by substitution or graphing.

• (7, -8)

• (-7, 8)

• (-7, -8)

• (7, 8)