Question

Розв’яжіть систему рівнянь 2х+у=7 х2 -ху=6

Answer 1

$\tt\displaystyle \left \{ {{2x+y=7} \atop {x^2-xy=6}} \right. \Longrightarrow \left \{ {{y=7-2x} \atop {x^2-xy=6}} \right. \\\\\\x^2-x(7-2x)=6\\\\x^2-7x+2x^2-6=0\\\\3x^2-7x-6=0\\\\D=(-7)^2-4*3*(-6)=49+72=121\\\\\sqrt{121}=11\\\\x_1=\frac{7-11}{2*3}=\frac{-4}{6}=-\frac{2}{3}\\\\\\x_2=\frac{7+11}{6}=\frac{18}{6}=3\\\\\\y_1=7-2*(-\frac{2}{3})=7+\frac{4}{3}=8\frac{1}{3}\\\\\\y_2=7-2*3=7-6=1$

ответ: (-2/3; 8 1/3); (3; 1)