Question

Розв"яжіть систему рівнянь
{х²+2ху+у²=4
6х-7у=19

Answer 1

Ответ:

$\left\{\begin{array}{l}x^2+2xy+x^2=4\\6x-7y=19\end{array}\right\ \ \left\{\begin{array}{lc}\dfrac{(19+7y)^2}{36}+2y\cdot \dfrac{19+7y}{6}+y^2-4=0\\\ x=\dfrac{19+7y}{6}\end{array}\right$

$\left\{\begin{array}{l}361+266y+49y^2+228y+84y^2+36y^2-144=0\\x=\dfrac{19+7y}{6}\end{array}\right\ \ \left\{\begin{array}{l}169y^2+494y+217=0\\x=\dfrac{19+7y}{6}\end{array}\right$

$\left\{\begin{array}{l}\ y_1=-\dfrac{7}{13}\ ,\ y_2=-\dfrac{31}{13}\\x=\dfrac{19+7y}{6}\end{array}\right\ \ \left\{\begin{array}{l}\ y_1=-\dfrac{7}{13}\ ,\ y_2=-\dfrac{31}{13}\\x_1=\dfrac{33}{13}\ ,\ x_2=\dfrac{5}{13}\end{array}\right\\\\\\Otvet:\ \ \Big(\ \dfrac{33}{13}\ ;\ -\dfrac{7}{13}\ \Big)\ ,\ \Big(\ \dfrac{5}{13}\ ;\ -\dfrac{31}{13}\ \Big)\ .$