Question

Прошу помочь, не знаю как решить $\left \{{{13x+6y=7} \atop {2x-4y=0}} \right.$

Answer 1

Решение и ответ:

$\displaystyle\[\left\{\begin{array}{l}13x+6y=7\\2x-4y=0\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}13x+6y=7\\2x=4y\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}13x+6y=7\\x=2y\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}13\cdot2y+6y=7\\x=2y\end{array}\right.\Leftrightarrow\]$$\displaystyle\[\left\{\begin{array}{l}26y+6y=7\\x=2y\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}32y=7\\x=2y\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}y=\frac{7}{{32}}\\\\x=2y\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}y=\frac{7}{{32}}\\\\x=2\cdot\frac{7}{{32}}\end{array}\right.\Leftrightarrow\left\{\begin{array}{l}y=\frac{7}{{32}}\\\\x=\frac{7}{{16}}\end{array}\right.\]$

Ответ: $\displaystyle \[x = \frac{7}{{16}};y = \frac{7}{{32}}\]$