[tex]\left\{\begin{matrix}
2x + 3y = 5 \: | \times 2 \\
5x + 2y = - 2 \: | \times ( - 3) \end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
4x + 6y = 10\\
- 15x - 6y = 6\end{matrix}\right.[/tex]
[tex]4x - 15x + 6y - 6y = 10 + 6[/tex]
[tex] - 11x = 16 \: | \times ( - 1)[/tex]
[tex]11x = - 16[/tex]
[tex]x = - \frac{16}{11} [/tex]
[tex]2x + 3y = 5[/tex]
[tex]2 \times ( - \frac{16}{11} ) + 3y = 5[/tex]
[tex] - \frac{32}{11} + 3y = 5[/tex]
[tex]3y = 5 + \frac{32}{11} \: | \times 11[/tex]
[tex]33y = 55 + 32[/tex]
[tex]33y = 87[/tex]
[tex]y = \frac{87}{33} [/tex]
[tex]y = \frac{29}{11} [/tex]
