Challenge Solving Systems of Equations

Where do these graphs intersect?

y = 7x + 9

2y + 2x = -18

• (5, 0)

• (-2, 18)

• (-2, -5)

• (1, -5)

• (5, -5)

How many solutions does the system have?

y = 2x -11

-3y = -6x -15

• One solution

• Infinitely many solutions

• No solution

• Two solutions

How many solutions does the system shown above have?

• None

• One

• Two

• Three

• Infinite

CHALLENGE! What value of a would make the system have no solutions?

y + 5= 3x

y = ax + 6

• 5

• 3

• 6

• -5

CHALLENGE! What value of b would make the system have infinite solutions?

2y + 10= 8x

y = 4x + b

• 2

• -5

• 4

• -10

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

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:

• 1 solution

• no solution

• many solutions

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