[tex]1)\left\{\begin{matrix}
x + y = 4\\
2x - y = - 1\end{matrix}\right.[/tex]
[tex]x + 2x = 4 - 1[/tex]
[tex] 3x = 3[/tex]
[tex]x = \frac{3}{3} [/tex]
[tex]x = 1[/tex]
[tex]x + y = 4[/tex]
[tex]1 + y = 4[/tex]
[tex]y = 4 - 1[/tex]
[tex]y = 3[/tex]
[tex]2)\left\{\begin{matrix}
3x + 2y = 7 \: | \times ( - 2)\\
- x + 4y = 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 6x - 4y = - 14\\
- x + 4y = 5\end{matrix}\right.[/tex]
[tex] - 6x - x = - 14 + 5[/tex]
[tex] - 7x = - 9 \: | \times ( - 1)[/tex]
[tex]7x = 9[/tex]
[tex]x = \frac{9}{7} [/tex]
[tex] - x + 4y = 5[/tex]
[tex] - \frac{9}{7} + 4y = 5 \: | \times 7[/tex]
[tex] - 9 + 28y = 35[/tex]
[tex]28y = 35 + 9[/tex]
[tex]28y = 44[/tex]
[tex]y = \frac{44}{28} [/tex]
[tex]y = \frac{11}{7} [/tex]
[tex]3)\left\{\begin{matrix}
5x + y = 4 \: | \times 2\\
3x - 2y = 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
10x + 2y = 8\\
3x - 2y = 5\end{matrix}\right.[/tex]
[tex]10x + 3x = 8 + 5[/tex]
[tex]13x = 13[/tex]
[tex]x = \frac{13}{13} [/tex]
[tex]x = 1[/tex]
[tex]3x - 2y = 5[/tex]
[tex]3 \times 1 - 2y = 5[/tex]
[tex]3 - 2y = 5[/tex]
[tex] - 2y = 5 - 3[/tex]
[tex] - 2y = 2 \: | \div ( - 2)[/tex]
[tex]y = - 1[/tex]
