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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
Your Input
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:
$$$y = \frac{\frac{34}{5}}{\frac{17}{5}} = 2$$$
$$$x = \frac{1 - \left(-2\right) \left(2\right)}{5} = 1$$$
Answer
$$$x = 1$$$A
$$$y = 2$$$A