Is there anyway to find the values for equation with two variables

Question

Is there mathematical anyway to find the values for equation with two variables? as example:

I have y = (20x+3)r+x and y is 50. then what is x and r values?

Answer 1

No. The equation with two variables $x$ and $r$

$$y=50=(20x+3)r+x$$ has infinitely many solutions. Notice that the equation is equivalent to $$(20r+1)x=50-3r$$ so if we pick $r\ne-\frac1{20}$ we find $x=\frac{50-3r}{20r+1}$.

Answer 2

There are three unknowns in your problem, namely $x,y,r$ and you only have two equations. So, here $$50=(20x+3)r+x$$ gives you a relation between $r$ and $x$. For example, assuming that $(20x+3) \ne 0$,$$r=\frac{50-x}{20 x+3}$$ you can select any $x$ and get avalue for $r$.

Answer 3

$y = (20x+3)r+x = 20xr+3r+x\\ 20y+3 = (20x+3)(20r+1)$

So you should find the factors of $20y+3$.