Question

resolva o sistema de equaçao
{4x²+2xy+y²=37
{2x-y=1
ME AJUDEM URGENTE SEREI GRATO!!!

Answer 1

$\begin{cases} 4x^2+2xy+y^2=37\cdots\cdots \textcircled{1}\\ 2x-y=1\cdots\cdots\cdots\cdots\cdots \textcircled{2} \end{cases}\\ \\ \text{Despejamos }y \text{ en }\textcircled{2}: \\ y=2x-1\cdots\cdots\cdots\cdots \textcircled{3}\\ \\ \text{Reemplazamos }\textcircled{3} \text{ en } \textcircled{1}:\\ 4x^2+2x(2x-1)+(2x-1)^2=37\\ 12x^2 - 6x + 1 = 37\\ 12x^2 - 6x -36=0\\ 2x^2-x-6=0\\ (2x+3)(x-2)=0\\ \\ \displaystyle x\in\left\{-\frac{2}{3},2\right\}$

Respuesta:
                  $\displaystyle \boxed{(x,y)\in\left\{\left(-\frac{2}{3},-\frac{7}{3}\right);(2,3)\right\}}$