+2666 Let \(\sqrt{x} = m\) and let \( \sqrt{y}=n\)
We now have a new system:
\(4m^2 + 9n^2 = 793 \ \ \ \ \ \ \ \ (i)\)
\(m + n = 13 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)\)
From \((ii)\), we have \(n = 13 - m \).
Plugging this into \((i)\) gives us \(4m^2 + 9(13 - m)^2 = 793\), which simplifies to \(13m^2 + 1521 - 234m=793\).
Subtracting \(793\) from both sides gives us \(13m^2 - 234m + 728 = 0\).
Now, solve for \(m\), square it, and plug it into both equations to make sure it works.
Good luck!
