3. Come up with a system of two equations with two unknowns $x$ and $y$, so that its solutions are only the following three pairs of numbers: $x=y=1, x=y=2$ and $x=3, y=4$. In the equations of the system, in addition to numbers and the unknowns $x$ and $y$ themselves, you are allowed to use parentheses, the equality sign $=$, standard arithmetic operations, and elementary functions.
Solution. For example, $\left\{\begin{array}{c}(x-1)(x-2)(x-3)=0 \\ (|x-1|+|y-1|)(|x-2|+|y-2|)(|x-3|+|y-4|)=0\end{array}\right.$