Cramer's Rule Calculator

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

Related calculators: System of Equations Calculator, System of Linear Equations Calculator

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Your Input

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

Solution

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

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

$$$x = -1$$$, $$$y = 3$$$A