Let x and y be the two integers.
Then x + y = -56 and x/y = 7
Solve second equation for x. So, x = 7y
Substitute in the first equation.
7y + y = 16 so 8y = -56
y = -56/8 = -7
y = -7
Find x, x + (-7) = -56 or x = -49
Check: -49+ (-7) = -56 and -49/-7 = 7