Question

Решите систему уравнений

Answer 1

$\left \{ {{2 x^{2} +3y^2=11|*(-2)} \atop {4 x^{2} +6y^2=11x}} \right. \left \{ {{-4 x^{2} -6y^2=-22} \atop {4 x^{2} +6y^2=11x}} \right. \left \{ {{0=-22+11x} \atop {2 x^{2} +3y^2=11}} \right. \left \{ {{11x=22} \atop {2 x^{2} +3y^2=11}} \right.$

$\left \{ {{x=22:11} \atop {2 x^{2} +3y^2=11}} \right. \left \{ {{x=2} \atop {2*2^2+3y^2=11}} \right. \left \{ {{x=2} \atop {3y^2=11-8}} \right. \left \{ {{x=2} \atop {y^2=3:3}} \right. \left \{ {{x=2} \atop {y^2=1}} \right. \left \{ {{x=2} \atop {y= \frac{+}{} 1}} \right.$


$\left \{ {{(x+6y)^2=7y} \atop {(x+6y)^2=7x|*(-1)}} \right. \left \{ {{(x+6y)^2=7y} \atop {-(x+6y)^2=-7x} \right. \left \{ {{0=7y-7x} \atop {(x+6y)^2=7y}} \right. \left \{ {{7x=7y} \atop {(x+6y)^2=7y}} \right. \left \{ {{x=y} \atop {(x+6x)^2=7x}} \right.$

$\left \{ {{x=y} \atop {(7x)^2=7x}} \right.\left \{ {{x=y} \atop {49x^2=7x}} \right. \left \{ {{x=y} \atop {49x^2-7x=0}} \right. \left \{ {{x=y} \atop {7x(7x-1)=0}} \right.$

x=y
x=0
x=$\frac{1}{7}$