2. The truncated difference of numbers $x$ and $y$ is the operation $x-y$, the result of which is equal to the usual difference $x-y$ if $x \geqslant y$, and zero if $x<y$.

Solve the system of equations $\left\{\begin{array}{l}2 x-y=0 \\ x+2 y=1\end{array}\right.$.
Solution. The first equation of the system is equivalent to the inequality $2 x \leqslant y$. Express $y$ from the second equation ( $y=(1-x) / 2$ ) and substitute it into the inequality.

$$
\frac{1-x}{2} \geqslant 2 x \Longleftrightarrow 1 \geqslant 5 x
$$

Thus, the system has an infinite number of solutions lying on the ray $\left\{\begin{array}{l}x \leqslant 1 / 5, \\ y=(1-x) / 2 .\end{array}\right.$

If solving the initial inequality with respect to $y$, an alternative form of the answer is obtained $\left\{\begin{array}{l}x=1-2 y, \\ y \geqslant 2 / 5 .\end{array}\right.$

Answer. $\left\{\begin{array}{l}x \leqslant 1 / 5, \\ y=(1-x) / 2\end{array}\right.$ or $\left\{\begin{array}{l}x=1-2 y, \\ y \geqslant 2 / 5 .\end{array}\right.$