Question

розв'яжіть систему рівнянь {3(х+у)+(х-у)=20
{5(х+у)-(х-у)=28 ​

Answer 1

Ответ:

$\left\{\begin{array}{l}3(x+y)+(x-y)=20\\5(x+y)-(x-y)=28\end{array}\right\ \ \left\{\begin{array}{l}u=x+y\\v=x-y\end{array}\right\ \ \left\{\begin{array}{l}3u+v=20\\5u-v=28\end{array}\right\ \oplus$

$\left\{\begin{array}{l}3u+v=20\\8u=48\end{array}\right\ \ \left\{\begin{array}{l}v=20-3u\\u=6\end{array}\right\ \ \left\{\begin{array}{l}v=20-18\\u=6\end{array}\right\ \ \left\{\begin{array}{l}v=2\\u=6\end{array}\right$

$\left\{\begin{array}{l}x+y=6\\x-y=2\end{array}\right\ \oplus \ominus \ \left\{\begin{array}{l}2x=8\\2y=4\end{array}\right\ \ \left\{\begin{array}{l}x=4\\y=2\end{array}\right\ \ \ \ Otvet:\ \ (\ 4\ ;\ 2\ )\ .$