Question

помогите решить систему уравнений​

Answer 1

Ответ:

x = 1; y = 0.

Пошаговое объяснение:

$\begin{equations*}\begin{cases}\frac{x+y}{2} - \frac{x-y}{3} = \frac{1}{6}\\\frac{x-y}{4} + \frac{x+y}{3} = \frac{7}{12}\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}\frac{(3(x+y) - 2(x-y)}{6} = \frac{1}{6}\\\frac{3(x-y)+4(x+y)}{12} = \frac{7}{12}\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}3(x+y) - 2(x-y)}= 1\\3(x-y)+4(x+y) = 7\end{cases}\end{equations*}\Leftrightarrow$

$\Leftrightarrow\begin{equations*}\begin{cases}3x+3y - 2x+2y = 1\\3x-3y+4x+4y = 7\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}x+5y = 1\\7x+y = 7\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}7x+35y = 7\\7x+y = 7\end{cases}\end{equations*}\Leftrightarrow$

$\Leftrightarrow\begin{equations*}\begin{cases}7x+35y = 7\\-34y = 0\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}7x+35y = 7\\y = 0\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}7x = 7\\y = 0\end{cases}\end{equations*}\Leftrightarrow\begin{equations*}\begin{cases}x = 1\\y = 0\end{cases}\end{equations*}$