Solving Systems of Equations All Methods

Identify which method for solving systems is being described by this fact: When the lines are parallel and do not intersect at any points the solution is No Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

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

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

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

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

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

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58

Solve for x and y by graphing.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

What are the solutions to the system of equations below?

• x = 4 and y = -2

• x = 4 and y = 2

• x = -4 and y = 2

• x = -4 and y = -2

Give the solution to the system.

• (3,1)

• (1,3)

• (-1,3)

• (1, -3)