Question

Розвяжіть систему
$2x + y = 7 \\ x ^{2} - xy = 6$
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Answer 1

Решение:

$\left \{ {{2x+y=7} \atop {x^{2}-xy=6}} \right. \\\left \{ {{y=7-2x} \atop {x^{2}-xy=6}} \right. \\x^{2}-x(7-2x)=6\\x^{2}-7x+2x^{2}=6\\x^{2}+2x^{2} -7x=6\\3x^{2}-7x=6\\3x^{2}-7x-6=0\\D=(-7)^{2}-4*3*(-6)=49+72=121=11^{2} \\D>0; 2-korni\\x_{1}=\frac{-(-7)+11}{2*3}=\frac{7+11}{6}=\frac{18}{6}=3\\x_{2}=\frac{-(-7)-11}{2*3}=\frac{7-11}{6}=\frac{-4}{6}=-\frac{2}{3}\\y_{1}=7-2x_{1}=7-2*3=7-6=1\\y_{2}=7-2x_{2}=7-2*(-\frac{2}{3})=7+\frac{4}{3}=\frac{21+4}{3}=\frac{25}{3}=8\frac{1}{3}$

Ответ: $(x_{1};y_{1})=(3;1)\\(x_{2};y_{2})=(-\frac{2}{3}; 8\frac{1}{3})$

$DK954$