Solution: The determinant of the system is

Since D = 0, we cannot solve for x and y in the form of (3) above. However, we can consider forms (1) and (2), since they do not involve division by zero. Evaluating the other determinants, we have

Thus (1) and (2) lead to

Because the contradictory equations (I) are implied by the system (H), this latter system has no simultaneous solution.
 

It can be shown that if the determinant of system (G) is zero, then (G) has no solution or an infinite number of solutions.
 
 

Tuesday, June 23, 1998