10.1. Find all solutions of the equation: $\sqrt{1-x}+\sqrt{2-y}=\sqrt{3 x+2 y-7}$.
Answer. $x=1, y=2$.

Solution. From considering the domain, it immediately follows that ${ }^{x \leq 1, y \leq 2}$ and $y \geq \frac{7-3 x}{2}$. Note that, for $x \leq 1$, we have $y \geq \frac{7-3 x}{2} \geq \frac{7-3}{2}=2$, and the inequalities become strict when $x<1$, so the only point in the domain will be $x=1, y=2$, which, as can be easily verified by substitution, is a solution to the equation.

Grading criteria. Correct answer guessed: 1 point. Domain correctly written: 1 point.