Systems of Equations and Number of Solutions

Solve the system of Equation (x,y)
−4x + 9y = 9
x − 3y = −6 

• (-9,-5)

• (-5,9)

• (9,5)

• (-5,-9)

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

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

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 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

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

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

What is the solution to the system of equations?

• No Solution

• (2, 0)

• Infinitely Many Solutions

• (0, 2)

What is the solution to the systems of equations shown in the graph?

• 1 Solution x=-1/2

• 1 Solution y=-1/2

• Many Solutions

• No Solution

What is the solution to the equations below ? y = 3x + 2 y = 3x - 5

• a. NO Solution because the slopes are the same and the y-intercepts are different.

• b. ONE Solution because the slopes are the same.

• c. MANY Solutions because the slopes are the same.

• d. No Solution because the y-intercepts are the same.