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Cramer's Rule: Solve 2x − 3y = −1 and 4x + 5y = 9

Use Cramer's rule to solve 2x − 3y = −1 and 4x + 5y = 9. Compute all three determinants and verify x = y = 1 in both equations.

Question

Solve this system with Cramer's rule:

{2x−3y=−14x+5y=9\begin{cases}2x-3y=-1\\4x+5y=9\end{cases}

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Evidence boundary

This page solves OpenStax College Algebra 2e, Section 7.8, Exercise 25. The equations and requested method are from that exercise; the determinants and substitutions are calculated here. Cramer's determinant ratios require a nonzero coefficient determinant.