2) 5x-y=1
3) x-5y=1
\[График\ проходит\ через\ точку\ с\]
\[координатами\ (0;1);k < 0:\]
\[y = - kx + 1.\]
\[И\ через\ точку\ (1;\ - 4):\]
\[при\ x = 1 \rightarrow y = - 4.\]
\[1)\ 5x + y = 1\]
\[y = - 5x + 1.\]
\[2)\ 5x - y = 1\]
\[y = 5x - 1.\]
\[3)\ x - 5y = 1\]
\[5y = x - 1.\]
\[4)\ x + 5y = 1\]
\[5y = - x + 1.\]
\[Нам\ подходит\ уравнение\ 1).\]
\[Ответ:1)\ 5x + y = 1.\]
\[\left\{ \begin{matrix} x - 7y = 20\ \ \ \\ 5x + 2y = 26 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 20 + 7y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5 \cdot (20 + 7y) + 2y = 26 \\ \end{matrix} \right.\ \]
\[100 + 35y + 2y = 26\]
\[37y = 26 - 100\]
\[37y = - 74\]
\[y = - 2.\]
\[x = 20 + 7 \cdot ( - 2) = 20 - 14 = 6.\]
\[\left\{ \begin{matrix} x_{0} = 6\ \ \ \\ y_{0} = - 2 \\ \end{matrix} \right.\ \]
\[x_{0} + y_{0} = 6 - 2 = 4.\]
\[Ответ:4)\ 4.\]
\[\left\{ \begin{matrix} 3x - 10y = 1\ \ | \cdot 3 \\ 9x + 2y = 67\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} 9x - 30y = 3 \\ 9x + 2y = 67 \\ \end{matrix} \right.\ ( - )\]
\[- 32y = - 64\]
\[y = 2.\]
\[3x = 1 + 10y = 1 + 10 \cdot 2\]
\[3x = 21\]
\[x = 7.\]
\[\left\{ \begin{matrix} x_{0} = 7 \\ y_{0} = 2 \\ \end{matrix} \right.\ \]
\[x_{0} - y_{0} = 7 - 2 = 5.\]
\[Ответ:3)\ 5.\]
\[\left\{ \begin{matrix} \frac{2x + 3y}{4} + \frac{3x - 2y}{5} = - \frac{1}{20}\ \ | \cdot 20 \\ \frac{3x + 4y}{2} - \frac{5x - y}{3} = \frac{43}{6}\ \ \ \ \ \ \ \ \ \ \ \ \ \ | \cdot 6 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 10x + 15y + 12x - 8y = - 1 \\ 9x + 12y - 10x + 2y = 43\ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 22x + 7y = - 1\ \ \ \ | \cdot 2 \\ - x + 14y = 43\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 44x + 14y = - 2 \\ - x + 14y = 43\ \ \ \\ \end{matrix} \right.\ ( - )\]
\[45x = - 45\]
\[x = - 1.\]
\[14y = 43 + x = 43 - 1\]
\[14y = 42\]
\[y = 3.\]
\[\left\{ \begin{matrix} x = - 1 \\ y = 3\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:( - 1;3).\]
\[Пусть\ x\ \frac{км}{ч} - скорость\ движения\]
\[пешком;\]
\[(x + 70)\ \frac{км}{ч} - скорость\ движения\]
\[на\ электричке.\]
\[3x\ км - прошли\ пешком;\]
\[2 \cdot (x + 70)\ км - проехали\ на\ электричке.\]
\[Весь\ путь\ равен\ 165\ км.\]
\[Составим\ уравнение:\]
\[3x + 2 \cdot (x + 70) = 165\]
\[3x + 2x + 140 = 165\]
\[5x = 165 - 140\]
\[5x = 25\]
\[x = 5\ \left( \frac{км}{ч} \right) - скорость\ движения\]
\[пешком.\]
\[5 \cdot 3 = 15\ (км) - группа\ прошла\ пешком.\]
\[Ответ:15\ км.\ \]
\[\left\{ \begin{matrix} x + 2y = 5\ \ \ \ \ \ \ \ \\ 0,5y + x = - 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} 2y = - x + 5\ \ \ \\ 0,5y = - x - 1 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - 0,5x + 2,5 \\ y = - 2x - 2\ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:( - 3;4).\]