Cramer's Rule Calculator

Solve the system of linear equations using Cramer's rule step by step

This calculator will solve the system of linear equations of any kind, with steps shown, using Cramer's rule.

Your Input

Solve $$$\begin{cases} x + 3 y = 8 \\ - 2 x + 5 y = 17 \end{cases}$$$ for $$$x$$$, $$$y$$$ using Cramer's rule.

Solution

Write down the augmented matrix: $$$\left[\begin{array}{ccc}1 & 3 & 8\\-2 & 5 & 17\end{array}\right]$$$.

Calculate the main determinant (for steps, see determinant calculator): $$$D = \left|\begin{array}{cc}1 & 3\\-2 & 5\end{array}\right| = 11$$$.

Substitute the $$$x$$$-column with the RHS (for steps in calculating the determinant, see determinant calculator): $$$D_{x} = \left|\begin{array}{cc}8 & 3\\17 & 5\end{array}\right| = -11$$$.

Hence, $$$x = \frac{D_{x}}{D} = \frac{-11}{11} = -1$$$.

Substitute the $$$y$$$-column with the RHS (for steps in calculating the determinant, see determinant calculator): $$$D_{y} = \left|\begin{array}{cc}1 & 8\\-2 & 17\end{array}\right| = 33$$$.

Hence, $$$y = \frac{D_{y}}{D} = \frac{33}{11} = 3$$$.

Answer

$$$x = -1$$$A

$$$y = 3$$$A