Systems of Equations Game
To solve a system of equations by substitution, first, solve one equation for one variable to express it in terms of the other. Then, substitute that expression into the second equation, which yields a single equation with only one variable that you can solve. Finally, substitute the solved variable back into one of the original equations to find the value of the other variable. Scroll down the page for a more detailed explanation.
 
The game will provide a system of two linear equations, with one equation already solved for a variable, making it suitable for the substitution 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 elimination method.
 

Systems of Equations

Solve for x and y using substitution.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Solve the system:

Answer:

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
To solve a system of equations by substitution, first, solve one equation for one variable to express it in terms of the other. Then, substitute that expression into the second equation, which yields a single equation with only one variable that you can solve. Finally, substitute the solved variable back into one of the original equations to find the value of the other variable.
Solve Systems of Equations
Here are the steps

1. Isolate a Variable:
   Choose one of the equations and solve it for one of the variables (either x or y).
   Example: If you have the equations x + 3y = 4 and x + y = 2, you could solve the second equation for x: x = 2 - y.
   
2. Substitute the Expression:
   Take the expression you found in Step 1 and substitute it into the other equation.
   Example: Substitute (2 - y) for x in the first equation: (2 - y) + 3y = 4.
   
3. Solve for the Remaining Variable:
   Simplify and solve the new equation for the single remaining variable.
   Example: 2 - y + 3y = 4 becomes 2 + 2y = 4. Subtracting 2 from both sides gives 2y = 2, so y = 1.
   
4. Find the Value of the Other Variable:
   Substitute the value you just found (e.g., y = 1) back into either of the original equations.
   Example: Using x + y = 2, substitute y = 1 to get x + 1 = 2, which means x = 1.
   
5. Check Your Solution:
   As a final step, substitute the values you found (e.g., x=1, y=1) into both original equations to ensure they are both true.
   Example:
   Equation 1: 1 + 3(1) = 4 (True)
   Equation 2: 1 + 1 = 2 (True)
    
   

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