Systems of Equations Word Problem Game

Systems of Equations Word Problem Quiz/Game
This game focuses on solving systems of equations word problems including a wide range of applications: Coins, Ticket Sales, Relative Motion, Mixture, Food & Sales, Geometry & Numbers, Money, Animals & Objects. Scroll down the page for a more detailed explanation.

 

 

How to Play the Systems of Equations Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Systems of Equations Word Problems
Solving systems of equations word problems is essentially a translation task: you are turning a story into math. Almost all of these problems involve two different “totals” that create two separate equations

Define Your Variables
Read the final question first. Whatever the problem is asking you to find should be your x and y.

Write Your Two Equations
Most problems follow a predictable pattern. One equation usually describes Quantity, and the other describes Value.

Choose a Solving Method
Once you have your equations, you have three main ways to find the answer:
A. The Substitution Method
Best when one variable is already “alone” (e.g., y = 2x).
Solve one equation for x or y.
Plug that expression into the other equation.
Solve for the remaining variable.

B. The Elimination Method
Best when equations are lined up in standard form (Ax + By = C).
Multiply one or both equations so that one variable has opposite coefficients (like 5x and -5x).
Add the equations together to “cancel out” that variable.
Solve for the one that is left.

C. The Graphing Method
Best for visualizing where the two conditions meet. The solution is the point of intersection (x, y).

The “Mental Math” Shortcut (The Gap Method)
For many “Coin” or “Ticket” problems, you can solve them in your head:
Assume the Minimum: Imagine all items are the cheaper version. (e.g., all 50 tickets are $5 children’s tickets = $250).
Find the Gap: Subtract that from the actual total. (If the total was $400, the gap is $150).
Find the Difference: How much more is an adult ticket than a child’s? ($10 - $5 = $5).
Divide: The Gap Difference = The higher-value item. (150 ÷ 5 = 30 adults).
 

This video gives a clear, step-by-step approach to explain how to solve systems of equations word problems.

• Show Video

 

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