\[\boxed{\text{1110.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ \left\{ \begin{matrix} \frac{x}{3} + \frac{y}{4} - 5 = 0\ \ \ | \cdot 12 \\ 2x - y = 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x + 3y = 60\ \ \ \ \ \ \\ 2x - y = 10\ \ | \cdot 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x + 3y = 60 \\ 6x - 3y = 30 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 10x = 90 \rightarrow x = 9 \\ y = 2x - 10\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[y = 2 \cdot 9 - 10\]
\[y = 8\]
\[Ответ:(9;8).\]
\[\textbf{б)}\ \left\{ \begin{matrix} 2x - 7y = 4\ \ \ \ \ \\ \frac{x}{6} - \frac{y}{6} = 0\ \ | \cdot 6 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 2x - 7y = 4\ \ \ \ \ \ \ \ \ \\ x - y = 0\ \ | \cdot ( - 2) \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 2x - 7y = 4 \\ - 2x + 2y = 0 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} - 5y = 4 \rightarrow y = - \frac{4}{5} = - 0,8 \\ x = y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[x = - 0,8\]
\[Ответ:( - 0,8;\ - 0,8).\]
\[\textbf{в)}\ \left\{ \begin{matrix} \frac{2x}{3} - \frac{y}{2} = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \cdot 6 \\ 3 \cdot (x - 1) - 9 = 1 - y \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x - 3y = 0\ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - 3 - 9 + y = 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x - 3y = 0\ \ \ \ \ \ \ \\ 3x + y = 13\ \ | \cdot 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x - 3y = 0\ \\ 9x + 3y = 39 \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 13x = 39 \rightarrow x = 3 \\ 3y = 4 \cdot 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 3 \\ y = 4 \\ \end{matrix} \right.\ \]
\[Ответ:(3;4).\]
\[\textbf{г)}\ \left\{ \begin{matrix} \frac{5x}{6} - y = - \frac{5}{6}\ \ \ | \cdot 6 \\ \frac{2x}{3} + 3y = - \frac{2}{3}\ | \cdot 3 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 5x - 6y = - 5\ \ \ | \cdot 3 \\ 2x + 9y = - 2\ \ \ | \cdot 2 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 15x - 18y = - 15 \\ 4x + 18y = - 4\ \ \ \ \\ \end{matrix} \right.\ ( + )\]
\[\left\{ \begin{matrix} 19x = - 19 \rightarrow x = - 1 \\ 6y = 5x + 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[6y = - 5 + 5\]
\[6y = 0\]
\[y = 0\]
\[Ответ:( - 1;0).\]