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 $\left\{\begin{array}{l}5 x \cdot(y+6)=0 \\ 2 x+3 y=1\end{array}\right.$.
# Solution.

The first equation of the system is equivalent to the inequality $5 x \leqslant y+6$. Express $y$ from the second equation $(y=(1-2 x) / 3)$ and substitute it into the inequality.

$$
5 x \leqslant \frac{1-2 x}{3}+6 \Longleftrightarrow 17 x \leqslant 19
$$

Thus, the system has an infinite number of solutions lying on the ray $\left\{\begin{array}{l}x \leqslant 19 / 17 \\ y=(1-2 x) / 3 .\end{array}\right.$

If solving the initial inequality with respect to $y$, an alternative form of the answer is obtained $\left\{\begin{array}{l}x=(1-3 y) / 2, \\ y \geqslant-7 / 17 .\end{array}\right.$

Answer. $\left\{\begin{array}{l}x \leqslant 19 / 17, \\ y=(1-2 x) / 3\end{array}\right.$ or $\left\{\begin{array}{l}x=(1-3 y) / 2, \\ y \geqslant-7 / 17 .\end{array}\right.$