[tex]a)\left\{\begin{matrix}
x + y = 5\\
x - y = - 1\end{matrix}\right.[/tex]
[tex]x + x + y - y = 5 - 1[/tex]
[tex]2x = 4[/tex]
[tex]x = \frac{4}{2} [/tex]
[tex]x = 2[/tex]
[tex]x + y = 5[/tex]
[tex]2 + y = 5[/tex]
[tex]y = 5 - 2[/tex]
[tex]y = 3[/tex]
[tex]b)\left\{\begin{matrix}
2x + 3y = 5\\
- 2x + y = - 1\end{matrix}\right.[/tex]
[tex]2x - 2x + 3y + y = 5 - 1[/tex]
[tex]4y = 4[/tex]
[tex]y = \frac{4}{4} [/tex]
[tex]y = 1[/tex]
[tex]2x + 3y = 5[/tex]
[tex]2x + 3 \times 1 = 5[/tex]
[tex]2x + 3 = 5[/tex]
[tex]2x = 5 - 3[/tex]
[tex]2x = 2[/tex]
[tex]x = \frac{2}{2} [/tex]
[tex]x = 1[/tex]
[tex]c)\left\{\begin{matrix}
3x - y = 4 \: | \times 2 \\
2x + 2y = 0\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
6x - 2y = 8\\
2x + 2y = 0\end{matrix}\right.[/tex]
[tex]6x + 2x - 2y + 2y = 8 + 0[/tex]
[tex]8x = 8[/tex]
[tex]x = \frac{8}{8} [/tex]
[tex]x = 1[/tex]
[tex]2x + 2y = 0[/tex]
[tex]2 \times 1 + 2y = 0[/tex]
[tex]2 + 2y = 0[/tex]
[tex]2y = - 2[/tex]
[tex]y = - \frac{2}{2} [/tex]
[tex]y = - 1[/tex]
[tex]d)\left\{\begin{matrix}
- x - 5y = 4 \: | \times 3 \\
3x - 2y = 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 3x - 15y = 12\\
3x - 2y = 5\end{matrix}\right. [/tex]
[tex] - 3x + 3x - 15y - 2y = 12 + 5[/tex]
[tex] - 17y = 17 \: | \div ( - 17)[/tex]
[tex]y = - 1[/tex]
[tex]3x - 2y = 5[/tex]
[tex]3x - 2 \times ( - 1) = 5[/tex]
[tex]3x + 2 = 5[/tex]
[tex]3x = 5 - 2[/tex]
[tex]3x = 3[/tex]
[tex]x = \frac{3}{3} [/tex]
[tex]x = 1[/tex]
[tex]e)\left\{\begin{matrix}
3x - 5y = - 4 \: | \times ( - 2) \\
6x - 2y = 8\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 6x + 10y = 8\\
6x - 2y = 8\end{matrix}\right.[/tex]
[tex] - 6x + 6x + 10y - 2y = 8 + 8[/tex]
[tex]8y = 16[/tex]
[tex]y = \frac{16}{8} [/tex]
[tex]y = 2[/tex]
[tex]6x - 2y = 8[/tex]
[tex]6x - 2 \times 2 = 8[/tex]
[tex]6x - 4 = 8[/tex]
[tex]6x = 8 + 4[/tex]
[tex]6x = 12[/tex]
[tex]x = \frac{12}{6} [/tex]
[tex]x = 2[/tex]
[tex]f)\left\{\begin{matrix}
2x + 5y = 1 \: | \times ( - 2)\\
3x + 10y = - 1\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 4x - 10y = - 2\\
3x + 10y = - 1\end{matrix}\right.[/tex]
[tex] - 4x + 3x - 10y + 10y = - 2 - 1[/tex]
[tex] - x = - 3 \: | \times ( - 1)[/tex]
[tex]x = 3[/tex]
[tex]2x + 5y = 1[/tex]
[tex]2 \times 3 + 5y = 1[/tex]
[tex]6 + 5y = 1[/tex]
[tex]5y = 1 - 6[/tex]
[tex]5y = - 5 \: | \div 5[/tex]
[tex]y = - 1[/tex]
[tex]g)\left\{\begin{matrix}
3x + 5y = 2 \: | \times ( - 3) \\
5x + 3y = 2 \: | \times 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 9x - 15y = - 6\\
25x + 15y = 10\end{matrix}\right.[/tex]
[tex] - 9x + 25x - 15y + 15y = - 6 + 10[/tex]
[tex]16x = 4[/tex]
[tex]x = \frac{4}{16} [/tex]
[tex]x = \frac{1}{4} [/tex]
[tex]3x + 5y = 2[/tex]
[tex]3 \times \frac{1}{4} + 5y = 2[/tex]
[tex] \frac{3}{4} + 5y = 2 \: | \times 4[/tex]
[tex]3 + 20y = 8[/tex]
[tex]20y = 8 - 3[/tex]
[tex]20y = 5[/tex]
[tex]y = \frac{5}{20} [/tex]
[tex]y = \frac{1}{4} [/tex]
[tex]h)\left\{\begin{matrix}
3x - 2y = 1 \: | \times 3 \\
4x - 3y = - 1 \: | \times ( - 2)\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
9x - 6y = 3\\
- 8x + 6y = 2\end{matrix}\right.[/tex]
[tex]9x - 8x - 6y + 6y = 3 + 2[/tex]
[tex]x = 5[/tex]
[tex]3x - 2y = 1[/tex]
[tex]3 \times 5 - 2y = 1[/tex]
[tex]15 - 2y = 1[/tex]
[tex] - 2y = 1 - 15[/tex]
[tex] - 2y = - 14 \: | \div ( - 2)[/tex]
[tex]y = 7[/tex]
[tex]i)\left\{\begin{matrix}
2x + 5y = 10 \: | \times 2 \\
7x - 2y = - 4 \: | \times 5\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
4x + 10y = 20\\
35x - 10y = - 20\end{matrix}\right.[/tex]
[tex]4x + 35x + 10y - 10y = 20 - 20[/tex]
[tex]39x = 0[/tex]
[tex]x = \frac{0}{39} [/tex]
[tex]x = 0[/tex]
[tex]2x + 5y = 10[/tex]
[tex]2 \times 0 + 5y = 10[/tex]
[tex]0 + 5y = 10[/tex]
[tex]5y = 10[/tex]
[tex]y = \frac{10}{5} [/tex]
[tex]y = 2[/tex]
