# System of Linear Equations Calculator

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan Elimination method or the 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. ## Solution 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): $$\left[\begin{array}{cc|c}5 & -2 & 1\\0 & \frac{17}{5} & \frac{34}{5}\end{array}\right]$$$Back-substitute: $$y = \frac{\frac{34}{5}}{\frac{17}{5}} = 2$$$