Answer
$(1,1)$
Work Step by Step
$\left\{\begin{array}{l}{y=\sqrt{x}}\\{y=2-x}\end{array}\right.$
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Restrictions: $x\geq 0,y\geq 0$
Substitute y into the second equation, square both sides
$\begin{aligned}\sqrt{x}&=2-x\\x&=4-4x+x^{2}\\0&=x^{2}-5x+4\\(x-4)(x-1)&=0\end{aligned}$
$\left[\begin{array}{ll}
x=1 & x=4\\
\text{... back -substitute} & \\
& \\
y=2-1 & y=2-4\\
y=1 & y=-2\\
& \text{discard,}\\
(1,1) & \text{negative} \\
&
\end{array}\right]$