Question

Решите, пожалуйста, уравнение.
$\left \{ {2(x+y)^{2}-7(x+y)+3=0 } \atop {2x - 3y = -1}} \right.$

Answer 1

Решим первое уравнение системы :

$2(x+y)^{2}-7(x+y)+3=0\\\\x+y=m\\\\2m^{2}-7m+3=0\\\\D=(-7)^{2}-4*2*3=49-24=25=5^{2}\\\\m_{1}=\frac{7-5}{4}=0,5\\\\m_{2} =\frac{7+5}{4}=3\\\\1)\left \{ {{x+y=0,5}|*(-2) \atop {2x-3y=-1}} \right. \\\\+\left \{ {{-2x-2y=-1} \atop {2x-3y=-1}} \right.\\ -------\\-5y=-2\\\\y_{1}=0,4\\\\x=0,5-y=0,5-0,4=0,1\\\\x_{1}=0,1$

$2)\left \{ {{x+y=3}|*3\atop {2x-3y=-1}} \right. \\\\+\left \{ {{3x+3y=9} \atop {2x-3y=-1}} \right.\\ -------\\5x=8\\\\x_{2}=1,6\\\\y=3-x=3-1,6=1,4\\\\y_{2}=1,4\\\\Otvet:\boxed{(0,1;0,4),(1,6;1,4)}$