Applying Systems of Linear Equations

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

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

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

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

• yes

• no

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Solve the system of equations.
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Two brothers went shopping. All shirts and all shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. Which system of equations represents the situation?

• 13x + 14y = 340
  7x + 7y = 165

• 6x + 7y = 175

• 7x + 7y = 175
  6x + 7y = 165

• x + y = 13
  165x + 175y = 14

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

• x + y = 315
  5x + 6y = 450

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20