Question

$\frac{2x+1}{y+3} =1 \frac{y}{x+2}$

Answer 1

$\begin{cases} \dfrac{2x+1}{y+3} = 1\\\\ \dfrac{y}{x+2} =-\dfrac{1}{2}\end{cases}\\\\\\\\\\ \dfrac{2x+1}{y+3} = 1\to~~multiplique~~cruzado\to~~ y+3=2x+1\to\\\\\\ y=2x+1-3\to~~ y=2x-2\\\\\\\\\\ \dfrac{y}{x+2} =-\dfrac{1}{2}\to~~\dfrac{2x-2}{x+2} =-\dfrac{1}{2}\to~~multiplique~~cruzado:\\\\\\-x-2=4x-4\to~~-x-4x=-2=4\to~~-5x=-2~(-1)\to\\\\\\ 5x=2\to~~\large\boxed{x= \frac{2}{5} }$




$y=2x-2\to~~y=2.\left( \dfrac{2}{5} \right)-2\to~~ y= \dfrac{4}{5} -2\to~~mmc=5\\\\\\ 5y=4-10\to~~ 5y=-6\to~~ \large\boxed{y=- \frac{6}{5} }\\\\\\\\\\\\ \Large\boxed{\boxed{S=\left\{ \frac{2}{5} ~; ~-\frac{6}{5} \right\}}}$