Systems of Equations Solver

LivePhysics™

System Input

System Size

Augmented Matrix

x	y	z	\|	b

Presets

Results

Classification

Unique Solution

Determinant

-1

Solution

x = 2

y = 3

z = -1

Step-by-Step Row Reduction

1. Initial augmented matrix

\left[\begin{array}{ccc|c}2 & 1 & -1 & 8 \\ -3 & -1 & 2 & -11 \\ -2 & 1 & 2 & -3\end{array}\right]

2. Swap R1 and R2

R_{1} \leftrightarrow R_{2}

3. R2 ← R2 - -0.6667·R1

R_{2} \leftarrow R_{2} - -0.6667 \cdot R_{1}

4. R3 ← R3 - 0.6667·R1

R_{3} \leftarrow R_{3} - 0.6667 \cdot R_{1}

5. Swap R2 and R3

R_{2} \leftrightarrow R_{3}

6. R3 ← R3 - 0.2000·R2

R_{3} \leftarrow R_{3} - 0.2000 \cdot R_{2}

7. Back substitution gives the solution

x = 2, \quad y = 3, \quad z = -1

Reference Guide

Free systems solver for 2x2 through 5x5 systems. Gaussian elimination with step-by-step row operations and solution classification.

Gaussian Elimination

primary

Unique Solutions

secondary

No Solution

times

tertiary

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