Question

Розвʼяжіть систему рівнянь:
x + 2y = 5,
x²+ 2ху - 3у²= -7.

Answer 1

Пояснення:

$\displaystyle\\\left \{ {{x+2y=5} \atop {x^2+2xy-3y^2=-7}} \right. \ \ \ \ \left \{ {{x=5-2y} \atop {(5-2y)^2+2*(5-2y)*y-3y^2=-7}} \right. \\\\\\\left \{ {{x=5-2y} \atop {25-20y+4y^2+10y-4y^2-3y^2=-7} \right.\ \ \ \ \left \{ {{x=5-2y} \atop {-3y^2-10y+32=0\ |*(-1)}} \right.$

$\displaystyle\\\left \{ {{x=5-2y} \atop {3y^2+10y-32=0}} \right. \ \ \ \ \left \{ {{x=5-2y} \atop {3y^2-6y+16y-32=0}} \right. \ \ \ \ \ \left \{ {{x=5-2y} \atop {3y*(y-2)+16*(x-2)=0}} \right. \\\\\\\left \{ {{x=5-2y} \atop {(y-2)(3y+16)=0}} \right. \ \ \ \ \ \left \{ {{x=5-2y} \atop {y-2=0\ \ \ \ 3y+16=0\ |:3\ \ \ \ \ \ \right. \left \{ {{x_1=1\ \ \ \ x_2=\frac{47}{3} } \atop {y_1=2\ \ \ \ y_2=-\frac{16}{3} }} \right. .$