Systems of Equations Game (Elimination)
A system of equations is simply a set of two or more equations with the same variables. “Solving” the system means finding the one unique point $(x, y)$ that makes all equations in the system true simultaneously. There are two main algebraic methods for finding this solution: Substitution, and Elimination. For substitution, solve one equation for a variable and substitute that expression into the other equation. For elimination, manipulate the equations so a variable cancels out when the equations are added or subtracted. Scroll down the page for a more detailed explanation.
 
The game will provide a system of two linear equations. Both equations are in Standard Form Ax + By = C and coefficients share a simple common multiple making it suitable for the elimination method. If you get an answer wrong, the game will show you the correct values for x and y. Check out this other Systems of Equations Game that may be more suitable for the substitution method.
 

Systems by Elimination

Solve the system of equations for x and y using the elimination method.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Solve for x and y:

Enter your solution:

x = y =

Check Next

Back to Menu

 

How to Play the Systems of Equations Game
This game is designed to help you master the process of solving systems of equations.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given two equations with variables x and y. Solve the systems of equations.
   
3. Enter Your Answer: Enter in the values for x and y. Remember to enter the negative symbol for negative numbers.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to solve the Systems of Equations
Method 1: Substitution
The substitution method is best when one of the equations already has a variable isolated (e.g., y = … or x = …).
The Steps:

1. Isolate: Solve one of the equations for either x or y. (Skip this step if a variable is already isolated.)
   
2. Substitute: Plug the expression from Step 1 into the other equation. This creates a new equation with only one variable.
   
3. Solve: Solve the new, one-variable equation (e.g., solve for x).
   
4. Back-Substitute: Plug the value you found in Step 3 back into the simplified equation from Step 1 to find the second variable (y).
    
   

Method 2: Elimination
The elimination method is best when both equations are in Standard Form (Ax + By = C), as it often requires less initial rearrangement than substitution.
The Steps:

1. Align: Arrange both equations so the terms line up vertically (x’s over x’s, y’s over y’s, constants over constants).
   
2. Multiply: If necessary, multiply one or both equations by a constant so that the coefficients of one variable are either equal or are opposites.
   
3. Add/Subtract: Add the two equations together. The variable with opposite coefficients will be eliminated, leaving a single-variable equation.
   
4. Solve & Back-Substitute: Solve the resulting equation, and then plug that value back into one of the original equations to find the second variable.
    
   

The video gives a clear, step-by-step approach to solve systems of equations using the elimination method.

• Show Video

 

Free Algebra Games
Distributive Property	Evaluate Algebraic Expressions	Evaluate Expressions (Exponents)
Simplify Algebraic Expressions	Solve Equations	Systems of Equations
Inequalities on the Number Line	Solve Inequalities	Multiply Binomials (y+b)(y+d)
Multiply Binomials (ay+b)(cy+d)	Solve Quadratic Equations

 

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