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.
$y = q x$ 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 $0$.