[tex]\left\{\begin{matrix}
2x + \frac{x + y}{2} = 4 \: | \times 2\\ \\
\frac{y - x}{2} + 3y = 10 \: | \times 2 \end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
4x + x + y = 8\\
y - x + 6y = 20\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
5x + y = 8\\
- x + 7y = 20 \: | \times 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
5x + y = 8\\
- 5x + 35y = 100\end{matrix}\right.[/tex]
[tex]5x - 5x + y + 35y = 8 + 100[/tex]
[tex]36y = 108[/tex]
[tex]y = \frac{108}{36} [/tex]
[tex]y = 3[/tex]
[tex]5x + y = 8[/tex]
[tex]5x + 3 = 8[/tex]
[tex]5x = 8 - 3[/tex]
[tex]5x = 5[/tex]
[tex]x = \frac{5}{5} [/tex]
[tex]x = 1[/tex]
