Mathematics

Cramer's rule lets you solve a system by turning it into a ratio of determinants—one for each variable. The key insight is that instead of manipulating equations, you swap out columns of the coefficient matrix with the constants, then divide determinants to isolate $x$ and $y$. This works because the determinant captures how the system "scales" solutions.

Cramer's rule lets you solve a system by turning it into a ratio of determinants—one for each variable. The key insight is that instead of manipulating equations, you swap out columns of the coefficient matrix with the constants, then divide determinants to isolate $x$ and $y$. This works because the determinant captures how the system "scales" solutions.