Is it possible to calculate $x$ and $y$?

Question

I am struggling with this.
If $p=frac{(x+y)}{2}$ and $q=frac{y}{x}$ and you know the values for $p$ and $q$, can you calculate what $x$ and $y$ are?
I tried $p=3.5$ and $q=2.5$ as an example. Given this $p$ and $q$, is the only possible solution $x=2$ and $y=5$? Or are there other solutions?
Thank you.

Robert Israel · Answer

$y = q x$ so your first equation becomes $p = frac{1+q}{2} x$, therefore (assuming $q ne -1$) the only solution is
$$ x = frac{2p}{1+q}, y = frac{2qp}{1+q}$$
where we need $p ne 0$.
Second case: $1+q = 0$.  Then if $p ne 0$, there is no solution, while if $p = 0$ the first equation becomes $0=0$ the solutions are $y=-x$, $x=$ anything except $0$.

Is it possible to calculate $x$ and $y$?

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