Cramer's Rule is an elegant and powerful 'cheat code' for solving systems of linear equations using determinants.

It works for any system that has a unique solution.

First, you calculate the 'main determinant,' D, using the coefficients of the x and y variables.

Next, you find the 'x-determinant,' Dx. You do this by taking the main determinant, but replacing the x-coefficients with the answer column.

Then, you find the 'y-determinant,' Dy, by replacing the y-coefficients with the answer column.

The solution is then shockingly simple.

The value of x is just Dx divided by D.

The value of y is just Dy divided by D.

While substitution or elimination might be faster for simple 2x2 systems, Cramer's Rule is incredibly powerful and systematic for larger systems.

It provides a clear, step-by-step formula for the answer, reducing the chance of logical errors.