How can I find 2 unknowns when they are in the same equations?

Question

So I have a question like this.

Given that $x + 1/y = 3/2$ and $y + 1/x = 1/6$, what is the value of $x / y$?

So basically I'm trying to get $x$ and $y$ on their own but I don't know how to because they are in both equations. I can't get my head around it. Does anyone know how to do it?

Thanks!

Answer 1

It is very easy, $x+\frac{1}{y}=\frac{3}{2}$ and $y+\frac{1}{x}=\frac{1}{6}$

So, $xy+1=\frac{3y}{2}$ and $xy+1=\frac{x}{6}$ , subtracting we get, $\frac{3y}{2}=\frac{x}{6}\implies \frac{x}{y}=9$