Solve Systems of Equations by Substitution Method

Determine if the system has one solution, infinitely many solutions, or no solution.

• One Solution

• Infinitely Many Solutions

• No Solution

Solve the following systems of equations using substitution:

x = 6

y = 2x - 3

• (6, 6)

• (6, 9)

• (9, 6)

• (9, 9)

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

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)

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

• (7, -8)

• (-7, 8)

• (-7, -8)

• (7, 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

Solve the system of equations using the substitution method.

• (-4, 11)

• (6.75, -2.25)

• No Solution

• (7.75, -.125)

Solve the system of equations using the substitution method.

• (1, 3)

• (-7, -4)

• Infinitely Many Solutions

• (4.25, -.65)