Given the system of equations
x(x+y)=9
y(x+y)=16
the value of xy can be written as a/b where a and b are positive coprime integers. Find a+b.
we see that 9/x = 16/y, so
y = 16/9 x
x(x + 16/9 x) = 9
25x^2 = 81
x = 9/5 or -9/5
y = 16/5 or -16/5
so, x+y = 5 or -5
check:
9/5 (5) = 9
16/5 (5) = 16
xy = 144/25
a+b = 169
same for - values