Challenge of the Week

The Department sponsors a problem solving competition for undergraduates at the university with a new challenge each week or so. We will feature some of the old problems on this blog, but changed slightly. Here is an example

Suppose that we have two rational numbers whose sum is negative 9 times their product and the sum is also negative 16 times their quotient. Find the two numbers.

x+ y = -9(xy)

x+y = -16(x/y)

Find x and y.