10-3. Solve the system $\left\{\begin{array}{c}2 y=|2 x+3|-|2 x-3| \\ 4 x=|y+2|-|y-2|\end{array}\right.$
Solution. Let's draw the graphs of the lines described by each equation. Each of them represents a broken line consisting of 3 segments.

First equation: $y=\frac{|2 x+3|-|2 x-3|}{2}$ $x-1.5 ; y=3$, when $-1.5 \leq x \leq 1.5 ; y=2 x$.

Second equation: $x=\frac{|y+2|-|y-2|}{4}$

$$
y2 ; y=1, \text { when }-2 \leq x \leq 2 ; y=x / 2 \text {. }
$$

As we can see, the graphs coincide on the interval $-1 \leq x \leq 1$. Therefore, the solution will be all points on the segment of the line $y=2 x$. Answer: $-1 \leq x \leq 1, y=2 x$.

Criteria. A complete answer without sufficient justification - 2 points.

![](https://cdn.mathpix.com/cropped/2024_05_06_e0fab438d09b07f8c89cg-1.jpg?height=523&width=394&top_left_y=1863&top_left_x=1528)
Full solution - 7 points.