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