Determine the conditions on a b c and d for which the system

Determine the conditions on a, b, c, and d for which the system of linear equations

ax+by= e

cx+dy=f

Solution

If ad bc is not equal to 0,  then the system has one unique point of intersection.

If the lines intersect at a unique point (i.e., solution exists and is unique)

Solution is -

ad- bc