Question

0.9. Решите систему уравнений​

Answer 1

Ответ:

$1)\ \left\{\begin{array}{l}2(x+y)-x=-6\\3x-(x-y)=0\end{array}\right\ \ \left\{\begin{array}{l}x+2y=-6\ |\cdot (-2)\\2x+y=0\end{array}\right\ \oplus \ \left\{\begin{array}{l}x+2y=-6\\-3y=12\end{array}\right\\\\\\\left\{\begin{array}{l}x=-6-2y\\y=-4\end{array}\right\ \ \left\{\begin{array}{l}x=2\\y=-4\end{array}\right\ \ \ Otvet:\ (2;-3)\ .$

$2)\ \left\{\begin{array}{l}x+5y=-2\\0,5x-y=6\ |\cdot 5\end{array}\right\ \oplus \ \left\{\begin{array}{l}5y=-2-x\\3,5x=28\end{array}\right\ \ \left\{\begin{array}{l}5y=-10\\x=8\end{array}\right\ \ \left\{\begin{array}{l}y=-2\\x=8\end{array}\right\\\\\\Otvet:\ (8;-2)\ .$

$3)\ \ \left\{\begin{array}{l}2x+3(x+y)=11\\7(x+3y)-4y=-23\end{array}\right\ \ \left\{\begin{array}{l}5x+3y=11\ |\cdot (-7)\\7x+17y=-23\ |\cdot 5\end{array}\right\ \oplus \ \left\{\begin{array}{l}5x=11-3y\\64y=-192\end{array}\right\\\\\\\left\{\begin{array}{l}5x=20\\y=-3\end{array}\right\ \ \left\{\begin{array}{l}x=4\\y=-3\end{array}\right\ \ \ \ \ Otvet:\ (4;-3)\ .$