Question

Решите систему уравнений: 9x^2+2y-6xy=6x-y^2 и 2x+5y=7

Answer 1

$\left \{ {{9x^{2}+2y-6xy=6x-y^{2}} \atop {2x+5y=7}} \right. \\\\\left \{ {{(9x^{2}-6xy+y^{2})+(2y-6x)=0 } \atop {2x+5y=7}} \right.\\\\\left \{ {{(3x-y)^{2}-2(3x-y)=0 } \atop {2x+5y=7}} \right.\\\\\left \{ {{(3x-y)(3x-y-2)=0} \atop {2x+5y=0}} \right.$

$1)\\\left \{ {{3x-y=0}|*5 \atop {2x+5y=7}} \right.\\\\+\left \{ {{15x-5y=0} \atop {2x+5y=7}} \right. \\------\\17x=7\\\\x=\frac{7}{17}\\\\y=3x=3*\frac{7}{17}=\frac{21}{17}=1\frac{4}{17}$

$2)\\\left \{ {{3x-y-2=0} \atop {2x+5y=7}} \right.\\\\\left \{ {{3x-y=2}|*5 \atop {2x+5y=7}} \right. \\\\+\left \{ {{15x-5y=10} \atop {2x+5y=7}} \right.\\ -------\\17x=17\\\\x=1\\\\y=3x-2=3*1-2=1\\\\Otvet:\boxed{(\frac{7}{17} \ ; \ 1\frac{4}{17}) \ , \ (1 \ ; \ 1)}}$