Question

Alguem poderia resolver esse sistema ?


2y - 4x = x/2
y - x = 10

Answer 1

Olá

$\displaystyle \left \{ {{2y-4x= \frac{x}{2}} \atop {y-x=10}} \right. \\\\\\\text{Passa o } \frac{x}{2} \text{ para o outro lado}\\\\\\\left \{ {{2y-4x- \frac{x}{2} = 0} \atop {y-x=10}} \right. \\\\\\\text{Faz o mmc}\\\\\left \{ {{2y- \frac{9x}{2} = 0 \atop {y-x=10}} \right. \\\\\\\text{Multiplique a }2^a\text{ linha por (-2), com isso conseguiremos eliminar o 'y' }\\\text{e encontrar o valor do x}\\\\\left \{ {{2y- \frac{9x}{2} = 0 \atop {-2y+2x=-20}} \right.\\\\\\\text{Some as duas equacoes}$

$\displaystyle \left \{ {{2y- \frac{9x}{2} = 0 \atop {\underline{-2y+2x=20}}} \right.\\~~~~~~~~~- \frac{5}{2}x =-20\\\\\ -\frac{5}{2}x=-20 ~~~ ~~~\cdot (-1)\\\\\frac{5}{2}x=20\\\\\\\text{Passa o } \frac{5}{2} \text{ Para o outro lado, multiplicando, so que inverte a posicao}\\\\\\x= 20\cdot \frac{2}{5} \\\\\\\boxed{x=8 }\\\\\\\text{Agora substitui o valor do 'x' que encontramos em qualquer uma }\\\text{das duas equacoes, e encontraremos o valor do 'y'}\\\text{Substituindo na 2}^a~\text{equacao}$

$\displaystyle y-x=10\\\\\\y-8=10\\\\\\y=10+8\\\\\\\boxed{y=18 }\\\\\\\\\\\text{Solucao}\\\\\\\\\boxed{S=\{x=8;y=18\}}$