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IM 8.4.15 Lesson: Writing Systems of Equations

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

Match each system of equations with the number of solutions the system has.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

For each situation:

  • Create a system of equations.
  • Then, without solving, interpret what the solution to the system would tell you about the situation.
Lin’s family is out for a bike ride when her dad stops to take a picture of the scenery. He tells the rest of the family to keep going and that he’ll catch up. Lin's dad spends 5 minutes taking the photo and then rides at 0.24 miles per minute until he meets up with the rest of the family further along the bike path. Lin and the rest were riding at 0.18 miles per minute. System of Equations:

Without solving, interpret what the solution to the system would tell you about the situation.

Noah is planning a kayaking trip. Kayak Rental A charges a base fee of $15 plus $4.50 per hour. Kayak Rental B charges a base fee of $12.50 plus $5 per hour. System of Equations:

Without solving, interpret what the solution to the system would tell you about the situation.

Diego is making a large batch of pastries. The recipe calls for 3 strawberries for every apple. Diego used 52 fruits all together. System of Equations:

Without solving, interpret what the solution to the system would tell you about the situation.

Flour costs $0.80 per pound and sugar costs $0.50 per pound. An order of flour and sugar weighs 15 pounds and costs $9.00. System of Equations:

Without solving, interpret what the solution to the system would tell you about the situation.

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:If your teacher gives you the data card:
  1. Silently read your card and think about what information you need to be able to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain how you are using the information to solve the problem. Continue to ask questions until you have enough information to solve the problem.
  4. Share the problem card and solve the problem independently.
  5. Read the data card and discuss your reasoning.
  1. Silently read your card.
  2. Ask your partner “What specific information do you need?” and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
  3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.
  4. Read the problem card and solve the problem independently.
  5. Share the data card and discuss your reasoning.
Use the space below to take notes on your discussion.

Here are a lot of systems of equations.




Without solving, identify 3 systems that you think would be the least difficult for you to solve. Explain your reasoning.

Without solving, identify 3 systems you think would be the most difficult for you to solve. Explain your reasoning.

Choose 4 systems to solve. At least one should be from your "least difficult" list and one should be from your "most difficult" list.

1st system with solution: ("least difficult")

2nd system with solution:

3rd system with solution:

4th system with solution: ("most difficult")

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