Answer
$(4,2)$
Work Step by Step
$\left\{\begin{array}{l}{y=\sqrt{x}}\\{y=6-x}\end{array}\right.$
Graphed with desmos.com/calculator.
Restrictions: $x\geq 0,y\geq 0$
Substitute y into the second equation, square both sides
$\begin{aligned}\sqrt{x}&=6-x\\x&=36-12x+x^{2}\\0&=x^{2}-13x+36\\(x-4)(x-9)&=0\end{aligned}$
(two factors of 36 whose sum is -13 ... are -4 and -9)
$\left[\begin{array}{ll}
x=4 & x=9\\
\text{... back -substitute} & \\
& \\
y=6-4 & y=6-9\\
y=2 & y=-3\\
& \text{discard,}\\
(4,2) & \text{negative} \\
&
\end{array}\right]$
