How does superimposing equations work

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Lets say i have 2 equations in the form ... = x

How would i superimpose them so that when i graph the equations i can see both lines in the same equation.
I thought i could just take each part and multiply them like this:

equation 1: ... = 0
equation 2: ... = 0

superimposed equation: (...) * (...) = 0

However when i tried this it did not work, the equations i used were:

$x\ -\ 3\ -\ \ 0\ \sqrt{-\frac{\left|\left|y\ -\ 2\right|-1\right|}{\left|y\ -\ 2\right|\ -\ 1}}=\ 0$

and

$y-1\cdot\ \sqrt{-\frac{\left|\left|x\ -\ 2\right|\ -\ 1\right|}{\left|x\ -\ 2\right|\ -\ 1}}=0$

The superimposition i tried doing (which didnt work) was:
$\left(y-1\cdot\ \sqrt{-\frac{\left|\left|x\ -\ 2\right|\ -\ 1\right|}{\left|x\ -\ 2\right|\ -\ 1}}\right)\cdot\left(x\ -\ 3\ -\ \ 0\ \sqrt{-\frac{\left|\left|y\ -\ 2\right|-1\right|}{\left|y\ -\ 2\right|\ -\ 1}}\right)=0$
however Desmos just shows nothing

If you plot them separately (i used Desmos for this) you will get a horizontal line and a vertical line,
superimposed they should thus form a 90 degree angle