System of Equations Calculator – Guide & Formulas
Solve systems of linear equations with 2 or 3 variables. Uses elimination, substitution, and matrix methods with complete steps.
Solve systems of simultaneous linear equations instantly. Supports both 2-variable systems and 3-variable systems with detailed step-by-step substitution and elimination breakdowns.
Key Takeaway
Use the free System of Equations Calculator to solve systems of linear equations with 2 or 3 variables. uses elimination, substitution, and matrix methods with complete steps. Get instant results with step-by-step explanations.
How to Use the System of Equations Calculator
- Choose the system size: 2 Variables (x, y) or 3 Variables (x, y, z).
- Input the coefficients of each equation in standard form.
- Analyze the exact solution values, steps, and system status (independent, dependent, or inconsistent).
The Formula
Variable Definitions
- x, y, z: The unknown variables to solve
- a, b, c: Input numeric coefficients
Solving a Two-Variable Supply Balance
Solve the system: 2x + y = 10 and x - y = 2.
- Step 1: Set equations: (1) 2x + y = 10 and (2) x - y = 2.
- Step 2: Use elimination by adding (1) and (2): (2x + x) + (y - y) = 10 + 2 => 3x = 12.
- Step 3: Solve for x: x = 4.
- Step 4: Substitute x = 4 into equation (2): 4 - y = 2 => y = 2. Solution: (4, 2).
Frequently Asked Questions
What is an inconsistent system?
An inconsistent system of equations has no solution. Geometrically, this happens when the lines are parallel and never intersect.
What is a dependent system?
A dependent system has infinitely many solutions. This happens when the equations represent the exact same line.
Can this solve non-linear systems?
This calculator is specifically designed for systems of linear equations (straight lines and flat planes).