Question

Решите систему уравнений

$left { {2x^2-xy-3y^2+x+y=6 atop 2x^2-5xy+3y^2+x-y=2} right.$

 

Answer 1

$left { {{(x+y)(2x-3y)+(x+y)=6} atop {(x-y)(2x-3y)+(x-y)=2}} right.\ left { {{(x+y)(2x-3y+1)=6} atop {(x-y)(2x-3y+1)=2}} right. \ left { {{frac{x+y}{x-y}=3} atop {2x^2-5xy+3y^2+x-y=2}} right. \ left { {{x+y=3(x-y)} atop {2x^2-5xy+3y^2+x-y=2}} right.\ left { {{x=2y} atop {8y^2-10y^2+3y^2+2y-y=2}} right.\ left { {{x=2y} atop {y^2+y-2=0}} right.$

$left { {{x=2y} atop {y=1}} right.$ или $left { {{x=2y} atop {y=-2}} right.$

$left { {{x=2} atop {y=1}} right.$ или $left { {{x=-4} atop {y=-2}} right.$

Ответ: (2; 1); (-4; -2)