Question

Suppose a and b are integers. How many solutions are there to the equation ab = 2a + 3b?

Answer 1

The equation is ab = 2a + 3b
Then,  ab = 2a + 3b
We will solve for "a" we get,
 
1) Add -2a to both the sides of the equation,
 
-2a + ab = 2a + -2a + 3b

On solving we get,

- 2a + ab = 3b

Again we have reached the same equation with which we started. We cannot determine the roots of the equation
 
Thus, There are no solutions to this equation.