Systems of Equations

A system of equations is shown below.

 $4x-5y=-10$  

 $2x-7y\ =4$  
Which operations on the system of equations will isolate the y quantity?

• Multiply the second equation by 2 and the result to the first equation.

• Multiply the second equation by -2 and the result to the first equation.

• Multiply the first equation by 7 and the second equation by -5 and add the resulting equations.

• Multiply the first equation by -7 and the second equation by -5 and add the resulting equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The substitution method will be used to solve this system of equations.

 $x+2y=7$  
 $2x-7y\ =3$  
Which equation would lead to a correct solution with this method?

•  $\left(7-2y\right)+2y=7$  

•  $\left(7+2y\right)+2y=7$  

•  $2\left(7-2y\right)-7y=3$  

•  $2\left(7+2y\right)-7y=3$  

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the solution to the system of equations below?

 $2x+y=7$  
 $3x+2y=16$  

• (2,5)

• (2,11)

• (-2,-11)

• (-2,11)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Caroline is considering two video game rental plans. Plan A can be modeled with the equation  $C=2n$  , and Plan B can be modeled with the equation  $C=n+6$  where C represents the cost in dollars and n represents the number of games rented each month. Which statement would justify selecting Plan A instead of selecting Plan B?

• Caroline rents exactly 7 games each month.

• Caroline rents exactly 6 games each month.

• Caroline rents exactly 6 or more games each month.

• Caroline rents from 1 to 5 games each month.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

What are the solutions to the system of equations below?

 $7x-5y=38$  
 $2x+10y=-12$  

• x = 4 and y = -2

• x = 4 and y = 2

• x = -4 and y = 2

• x = -4 and y = -2

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Tags

CCSS.8.EE.C.8A

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

• (1, 5)
• (5, 1)
• (0.25, 2)
• ∅

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

• yes
• no

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

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.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes
• 90 minutes
  2x + 4y = 315
• 60 minutes
  3x + 4y = 450
• 30 minutes

Tags

CCSS.8.EE.C.8C

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

Tags

CCSS.8.EE.C.8B