7.1.2

Use Cramer’s rule to solve x+y=a and rx+sy=b for x and y (with r, s, a, and b as parameters).

The matrix form of these equations is : The first column is the x coefficients while the second column is the y coefficients. The last column will be referred to as the right hand side.

Recall the definition of the determinant for a 2X2 matrix:

Cramer’s rule sets up the following formulae:

The top matrix in these fractions is composed in the following manner:

When solving for x, use the right hand side and the coefficients of y. When solving for y, use the coefficients of x and the right hand side.

The bottom matrix in these fractions is the cofactor matrix (the coefficients of x and y):

©James Reese [1998]