Systems of Equations with Steps

Aiden, Ethan, and Aria were having a friendly competition to solve a problem using substitution. Suddenly, they noticed an error in one of the steps. Can you help them identify which line contains the error?

• Line A

• Line B

• Line C

• Line D

Our friends Liam, Zoe, and Anika were watching Belinda solve a system of equations. Suddenly, they noticed an error! Can you spot which line contains the mistake?

• Line C

• Line D

• Line A

• Line E

• Line B

Evelyn, Zoe, and Nora are planning a big party at the Country Buffet restaurant. The restaurant has tables that seat 6 people and booths that can seat 4 people. They counted 38 seating units in total, which can accommodate 188 people. They started a fun challenge to figure out the number of tables, t, and the number of booths, b, at the restaurant. Can you help them solve this challenge?

• 4t=386 b=188

• t+b=38 6t+4b=188

• t+b=188 6t+4b=38

• t+b=38 4t+6b=188

Imagine this, Nora, Avery, and Daniel are playing a game of 'Treasure Hunt'. Nora finds a treasure chest filled with quarters and dimes amounting to $6.80. Avery notices that the number of dimes is 3 times the number of quarters. Can you help Daniel figure out a system of equations to find 'q', the number of quarters, and 'd', the number of dimes, in the treasure chest?

• q=3+d 0.25q+0.10d=6.80

• d=3+q q+d=6.80

• q=3d 0.25q+0.10d=6.80

• q=3d q+d=6.80

Imagine you're in a detective club with Ava, Nora, and Henry. Mrs. Ochoa just handed you a piece of work to investigate. Can you spot where the mystery student might have made a mistake?

• Line D

• Line A

• Line B

• Line C

• Line E

Abigail, Sophia, and Lily are on a treasure hunt. They found a mysterious note with two equations: 3x+2y=8 and 4y=-6x+16. They believe solving these equations will lead them to the treasure. Can you help them figure out if these equations have:

• solution

• no solution

• many solutions

Two burgers and one hotdog cost $4.82. At the same price, one burger and two hotdogs cost $3.70. How much does a hotdog cost?

Evaluate responses using AI:

OFF

If a system of linear equations has one solution, what does this mean about the two lines? The two lines......

• are parallel

• are the same line 

• intersect once

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

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5