System of Linear Equations Elimination and Substitution

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 for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

What is the solution to the system?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

Find the solution to the system of equations:
3x + 2y = 16
y = -7x + 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

y = -6x + 5
-2x + y = 5

• (-3, -6)

• (-6, 3)

• (0, 5)

• (-3, 5)

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

• yes

• no

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

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 8)