Suppose $x$ and $y$ are integers such that $xy+5x+4y=-5$. Find the greatest possible value of $y$.

10

Step-by-step explanation:

xy + 5x + 4y = -5

(x + 4) y + 5x = -5

(x + 4) y = -5x − 5

y = -5 (x + 1) / (x + 4)

For y to be large as possible, (x + 1) / (x + 4) must be negative.  That means -4 < x < -1.  So x is either -2 or -3.

The possible values of y are:

y = -5 (-2 + 1) / (-2 + 4) = 5/2 (not an integer).

y = -5 (-3 + 1) / (-3 + 4) = 10.