Solve Following System of Equations Calculator

This calculator solves systems of linear equations using the substitution and elimination methods. It handles 2x2, 3x3, and larger systems with step-by-step solutions.

How to Use This Calculator

To solve a system of equations:

Enter the coefficients and constants for each equation
Select the number of variables (2-5)
Click "Calculate" to see the solution
Review the step-by-step solution and chart visualization

Note: The calculator uses floating-point arithmetic which may produce small rounding errors. For exact solutions, consider using symbolic computation tools.

Solving Methods Explained

Substitution Method

The substitution method involves solving one equation for one variable and substituting this expression into the other equations. This reduces the system to a simpler form that can be solved with basic algebra.

Elimination Method

The elimination method combines equations to eliminate one variable at a time. This is typically done by adding or subtracting equations to create new equations with fewer variables.

Matrix Method

For larger systems, the calculator uses matrix operations including Gaussian elimination and back substitution to find solutions.

Matrix Form: A system of linear equations can be represented as AX = B, where A is the coefficient matrix, X is the solution vector, and B is the constant vector.

Worked Examples

Example 1: 2x2 System

Solve:
2x + 3y = 8
4x - y = 3

Solution: x = 1, y = 2

Example 2: 3x3 System

Solve:
x + y + z = 6
2x - y + z = 3
x - 2y + 3z = 11

Solution: x = 2, y = 1, z = 3

Frequently Asked Questions

How many equations can this calculator solve?: This calculator can solve systems with 2 to 5 variables and equations.
What if the system has no solution?: The calculator will indicate if the system is inconsistent (no solution) or dependent (infinitely many solutions).
Can I solve nonlinear systems with this calculator?: No, this calculator is designed for linear systems only. For nonlinear systems, consider using numerical methods or graphing.
How accurate are the solutions?: The calculator uses floating-point arithmetic which may produce small rounding errors. For exact solutions, consider using symbolic computation tools.