System of Linear Equations Calculator

Solve the system of linear equations step by step

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan elimination method, the inverse matrix method, or Cramer's rule.

Related calculator: System of Equations Calculator

Comma-separated, for example, x+2y=5,3x+5y=14.
Leave empty for autodetection or specify variables like x,y (comma-separated).

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Solve $$$\begin{cases} 5 x - 2 y = 1 \\ x + 3 y = 7 \end{cases}$$$ for $$$x$$$, $$$y$$$ using the Gauss-Jordan Elimination method.


Write down the augmented matrix: $$$\left[\begin{array}{cc|c}5 & -2 & 1\\1 & 3 & 7\end{array}\right]$$$.

Perform the Gauss-Jordan elimination (for steps, see Gauss-Jordan elimination calculator): $$$\left[\begin{array}{cc|c}5 & -2 & 1\\0 & \frac{17}{5} & \frac{34}{5}\end{array}\right]$$$.


$$$y = \frac{\frac{34}{5}}{\frac{17}{5}} = 2$$$

$$$x = \frac{1 - \left(-2\right) \left(2\right)}{5} = 1$$$


$$$x = 1$$$A

$$$y = 2$$$A