[tex]a)\left\{\begin{matrix}
2x - 3y = - 1\\
x + 3y = 4\end{matrix}\right.[/tex]
[tex]2x + x = - 1 + 4[/tex]
[tex]3x = 3[/tex]
[tex]x = \frac{3}{3} [/tex]
[tex]x = 1[/tex]
[tex]x + 3y = 4[/tex]
[tex]1 + 3y = 4[/tex]
[tex]3y = 4 - 1[/tex]
[tex]3y = 3[/tex]
[tex]y = \frac{3}{3} [/tex]
[tex]y = 1[/tex]
[tex]b)\left\{\begin{matrix}
- 3x + y = 5\\
x - y = 7\end{matrix}\right.[/tex]
[tex] - 3x + x = 5 + 7[/tex]
[tex] - 2x = 12 \: | \div ( - 2)[/tex]
[tex]x = - 6[/tex]
[tex]x - y = 7[/tex]
[tex] - 6 - y = 7[/tex]
[tex] - y = 7 + 6[/tex]
[tex] - y = 13 \: | \times ( - 1)[/tex]
[tex]y = - 13[/tex]
[tex]c)\left\{\begin{matrix}
x - 2y + 4 = 0\\
2x + y = - 1\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
x - 2y = - 4\\
2x + y = - 1 \: | \times 2\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
x - 2y = - 4\\
4x + 2y = - 2\end{matrix}\right.[/tex]
[tex]x + 4x = - 4 - 2[/tex]
[tex]5x = - 6[/tex]
[tex]x = - \frac{6}{5} [/tex]
[tex]2x + y = - 1[/tex]
[tex]2 \times ( - \frac{6}{5} ) + y= - 1[/tex]
[tex] - \frac{12}{5} + y = - 1 \: | \times 5[/tex]
[tex] - 12 + 5y = - 5[/tex]
[tex]5y = - 5 + 12[/tex]
[tex]5y = 7[/tex]
[tex]y = \frac{7}{5} [/tex]
[tex]d)\left\{\begin{matrix}
x + 2y = 0 \: | \times ( - 2)\\
2x + y = 1\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 2x - 4y = 0\\
2x + y = 1\end{matrix}\right.[/tex]
[tex] - 4y + y = 0 + 1[/tex]
[tex] - 3y = 1 \: | \times ( - 1)[/tex]
[tex]3y = 1[/tex]
[tex]y = \frac{1}{3} [/tex]
[tex]2x + y = 1[/tex]
[tex]2x + \frac{1}{3} = 1 \: | \times 3[/tex]
[tex]6x + 1 = 3[/tex]
[tex]6x = 3 - 1[/tex]
[tex]6x = 2[/tex]
[tex]x = \frac{2}{6} [/tex]
[tex]x = \frac{1}{3} [/tex]
[tex]e)\left\{\begin{matrix}
x = 2\\
2x - 3y = 1\end{matrix}\right.[/tex]
[tex]2 \times 2 - 3y = 1[/tex]
[tex]4 - 3y = 1[/tex]
[tex] - 3y = 1 - 4[/tex]
[tex] - 3y = - 3 \: | \div ( - 3)[/tex]
[tex]y = 1[/tex]
