+1537 The system of equations
\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1
has exactly one solution. What is $z$ in this solution?
+129852 \(\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1 \)
Either x = 0 or y, z = 0
But the second cannot be true because it would make the last fraction undefined
So x = 0
And (assuming integer solutions for y, z )
(yz) / (y + z) = 1
yz = y + z
zy - z = y
z ( y - 1) = y
z = y / (y -1)
y z
2 2
z = 2
