Simultaneous Radical Equations!
Algebra
Level
5
\[\large \begin{align} x+\sqrt{y}&=11 \\ y+\sqrt{x}&=7 \end{align}\]
Let \(n\) be the number of real pairs \((x, y)\) to the above system of equations. Define these solution pairs as \((x_1, y_1), \ldots, (x_n, y_n)\). Let
\[S=\displaystyle \sum_{i=1}^n \left(x_i + y_i\right).\]
Find \(n+S\).
by
Sharky Kesa