3. Solve the system of equations:

$$
\begin{aligned}
\frac{1}{2}\left(y+\frac{x}{2}\right)-\frac{1}{5}(x+2) & =1.1 \\
x-2 y+4 & =\frac{1}{4}\left(2 x+3\left(y-\frac{1}{2}\right)\right)
\end{aligned}
$$
3. First, we simplify both equations. The first is transformed into $10 y+5 x-4 x-8=22$ or $10 y+x=30$, and the second into $8 x-16 y+32=4 x+6 y-3$ or $4 x-22 y=-35$. We solve the system using one of the methods. If we use the substitution method, we express $x=30-10 y$ from the first equation and substitute it into the second equation: $4(30-10 y)-22 y=-35$. From this, we express $y=\frac{5}{2}$. Then we calculate $x=5$.

Simplification of the first equation: $10 y+x=30$. .1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_40efadbcfacda9b65264g-07.jpg?height=63&width=1639&top_left_y=894&top_left_x=206)

Correct solving of the system.......................................................................................

Solution of the system: $x=5, y=\frac{5}{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .1+1$ point