Linear Equation Solver
Solve systems of 2 or 3 linear equations with step-by-step solutions, graphical visualization, and downloadable results
2 Variables
3 Variables
Equation 1
x
+
y
=
Equation 2
x
+
y
=
Solution
–
Solution Distribution
Graphical Solution
About Linear Equation Solver
What is a System of Linear Equations?
A system of linear equations is a collection of two or more linear equations involving the same set of variables. The solution to the system is the set of variable values that satisfy all equations simultaneously.
Types of Systems
- 2-Variable System: Two equations with variables x and y
- 3-Variable System: Three equations with variables x, y, and z
Solution Methods
Our calculator uses the following methods:
For 2-Variable Systems: Cramer’s Rule or Elimination method
For 3-Variable Systems: Cramer’s Rule or Gaussian elimination
How to Use This Calculator
- Select 2 or 3 variables based on your system
- Enter the coefficients for each equation
- Click “Solve Equations” to see the solution
- View step-by-step solution and visualization
- Download results for your records
Example Problems
2-Variable Example:
2x + 3y = 7
x - y = 1
Solution: x = 2, y = 1
3-Variable Example:
x + y + z = 6
2y + 5z = -4
2x + 5y - z = 27
Solution: x = 5, y = 3, z = -2