Can a variable appear as a denominator in a linear equation or is the system non-linear?

Question

I am trying to figure out whether the following equation is non-linear or if it's linear, how would I solve it?

$x+\frac{2}{y}=0$

It can be rewritten as $x+y^{-2}=0$ so I guess if this is non-linear.

Answer 1

It is non-linear, and the criteria of linearity I've put in answer to your previous question. Here $f(x,y) = x+\frac2y$ and for $\alpha = 1,\beta = 1$ we have $$ f(x'+x'',y'+y'') = x'+x''+\frac2{y'}+\frac2{y''}\neq x'+x''+\frac2{y'+y''} = f(x',y')+f(x'',y'') $$ thus the equation is non-linear.

Saw the possible misprint in your question: $\frac2y\neq y^{-2} = \frac1{y^2}$.