Question

sistema de equação do segundo grau método de substituição

Answer 1

$\begin{cases} \dfrac{x}{y}= \dfrac{1}{2}~~(i)\\\\ x+y^2=18~~(ii)\end{cases}\\\\\\ y=2x~(y~isolado~da~equacao~i)\\\\\\ x+(2x)^2=18~~(e~substituido~na~eq.~ii)\\ x+4x^2=18\\ 4x^2+x-18=0\\\\ x_1=2~~e~~x_2=-\dfrac{9}{4}\\\\\\ para~x=2,~y=?~~~~~~~~~~para~x= -\dfrac{9}{4} ,~y=?\\\\ y=2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=2x\\ y=2\cdot2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=2\cdot\left(- \dfrac{9}{4} \right)\\\\ y_1=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y_2=- \dfrac{9}{2}$

Portanto:

$\large\boxed{\boxed{\text{S}=\left\{\left(2,4\right);\left(- \dfrac{9}{4},- \dfrac{9}{2}\right)\right\} }}$