Question

como resolver : x-2y=2 e 3x-2y=21/4

Answer 1

$sistema~de~equacoes~do~primeiro~grau\\\\x-2y=2~~~~~~~~~equacao~I\\\\3x-2y= \frac{21}{4} ~~~~~~~~equacao~II\\ \\ multiplique~uma~das~equacoes~por~(-1)~e~utilize~o~metodo~da~adicao:\\ \\ equacao~I\\ \\ x-2y=2(-1)~=~-x+2y=-2\\ \\ some~as~duas~equacoes:\\ \\ -x+2y=-2\\ ~~3x-2y~=\frac{21}{4} \\ -------\\ 2x+0=-2+\frac{21}{4} \\ \\ 2x=-2+\frac{21}{4} \\ \\ mmc=4\\ \\ 2x=\frac{-8+21}{4} =\frac{13}{4}$

$2x=\frac{13}{4} \\ \\ x=\frac{13}{4} .\frac{1}{2} \\ \\ x=\frac{13}{8} \\ \\ substitua~o~valor~de~x=\frac{13}{8}~em~uma~das~equacoes:\\ \\ equacao~II\\ \\ 3x-2y=\frac{21}{4} \\ \\ 3.\frac{13}{8} -2y=\frac{21}{4} \\ \\ \frac{39}{8} -2y=\frac{21}{4}$

$-2y=\frac{21}{4} -\frac{39}{8} \\ \\ mmc=8\\ \\ -2y=\frac{42-39}{8} =\frac{3}{8} \\ \\ -2y=\frac{3}{8} (-1)\\ \\ 2y=-\frac{3}{8} \\ \\ y=-\frac{3}{8} .\frac{1}{2} =-\frac{3}{16} \\ \\ y=-\frac{3}{16} \\ \\ S:(x=\frac{13}{8} ;~~~y=-\frac{3}{16} )$