Linear Systems of Equations with Graphing

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

Give the solution to the system

• (3,1)

• (1,3)

• (-1,3)

• No solution

Does the following system have One Solution, No Solution, or Infinite Solutions.  
y = 4x + 8
y = -5x + 3

• One solution

• No solution

• Infinite solution

The same line on a graph, has how many solutions?

• One solution

• Infinite solutions

• No solution

Intersecting lines have how many solutions?

• One solution

• No solutions

• Infinite solutions

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)

• (1, -4)

• (-4, 1)

• (4, -1)

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

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Which of the following are ways to solve systems of equations? 

• Graphing

• Substitution

• Elimination

• All of the above

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

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

• yes

• no