System of Equations Solver
Solve 2-variable and 3-variable linear equations with step-by-step solutions and graphical visualization
2 Variables
3 Variables
Equation 1
x
+
y
=
Equation 2
x
+
y
=
Solution
–
Solution Distribution
Graphical Solution
About System of Equations Solver
What is a System of Equations?
A system of equations is a collection of two or more equations with the same set of variables. In a linear system, each equation is linear (first degree).
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: Elimination or Substitution method
For 3-Variable Systems: Gaussian elimination or Cramer’s Rule
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