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.
 

 

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

• Algebraic Expressions

  Evaluate Algebraic Expressions
  Evaluate Expressions (Exponents)
  

  Distributive Property
  Distributive Property (Exponents)
  

  Simplify Algebraic Expressions
  Add or Subtract Polynomials
  

  Multiply Binomials (y+b)(y+d)
  Multiply Binomials (ay+b)(cy+d)
  

  Factor Linear Expressions
  Factor Binomials
  Factor Difference of Two Squares
  Factor Perfect Square Trinomials
  Factor Trinomials
  

• Algebraic Equations

  Solve Equations (1-step or 2-step)
  Solve Equations with variables on both sides
  Combine Like Terms & Solve Equations (2(3x-2) + 9 = -5x)
  

  Solve for a Variable (add or subtract)
  Solve Literal Equations (multiply or divide)
  

  Standard Form to Slope-Intercept Form
  Slope-Intercept Form to Standard Form
  

  Solve Quadratic Equations (a = 1)
  Solve Quadratic Equations (a > 1)
  Solve Quadratic Equations (use the quadratic formula)
  

  Solve Systems of Equations (by substitution)
  Solve Systems of Equations (by elimination)
  

• Algebraic Inequalities

  Inequalities on the Number Line (may not work well on the mobile)
  Solve Inequalities (1-step or 2-step)
  

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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