Question

развязать систему уравнений:
x-3y=4
xy-6y=1

Answer 1

$\left\{\begin{array}{l}x-3y=4\\xy-6y=1\end{array}\right\\\\\\\left\{\begin{array}{l}x=3y+4\\(3y+4)\cdot y-6y=1\end{array}\right\\\\\\\left\{\begin{array}{l}x=3y+4\\3y^{2} +4y-6y=1\end{array}\right\\\\\\\left\{\begin{array}{l}x=3y+4\\3y^{2}-2y-1=0\end{array}\right\\\\3y^{2} -2y-1=0\\\\D=(-2)^{2} -4\cdot 3\cdot (-1)=4+12=16=4^{2}\\\\y_{1} =\dfrac{2-4}{6}=-\dfrac{1}{3}\\\\y_{2} =\dfrac{2+4}{6}=1\\\\x_{1}=3y_{1}+4=3\cdot(-\dfrac{1}{3} )+4=-1+4=3\\\\x_{2} =3y_{2}+4=3\cdot1+4=3+4=7$

$Otvet:\boxed{(3 \ ; \ -\dfrac{1}{3}) \ , \ (7 \ ; \ 1)}$