If a system of linear equations with the same number of equations as unknowns has a unique solution, that solution may be found using ratios of various determinants. The following example of a 3 by 3 system illustrates the rule.

To solve this system, where , , and are variables and all other letters represent known real numbers

consider the following four determinants. (Evaluate determinants using the methods of 7.4.)

If , the system does not have a unique solution. If , the solution to the system of equations is , , and .

Example: Solve

, ,

Thus, the solution of the system is , , .

Last updated August 2, 1997. Comments?