Question

Ajudem por favor isolando uma variável

Answer 1

$a)~metodo~da~adicao~(multiplique~uma~das~equacoes~por~(-1):\\\\~~~~~~~~-x-y=3\\~+~~~~~3x+y=1\\~~~~~~~~------\\~~~~~~~~~2x+0=4\\\\2x=4\\\\x=\frac{4}{2}\\\\x=2\\\\substitua~(x=2)~em~uma~das~equacoes\\\\3x+y=1\\\\3.2+y=1\\\\6+y=1\\\\y=1-6\\\\y=-5~~~~~~~~~~~~~~S=(x=2;~~y=-5)$

$b)~metodo~da~adicao:~multiplique~a~segunda~equacao~por~2\\\\~~~~~~~~~~~~~x+2y=12\\~+~~~~~~~6x-2y=44\\~~~~~~~~~--------\\~~~~~~~~~~~7x+~0=~56\\\\7x=56\\\\x=\frac{56}{7}\\\\x=8\\\\substitua~(x=8)~em~uma~das~equacoes\\\\x+2y=12\\\\8+2y=12\\\\2y=12-8\\\\2y=4\\\\y=\frac{4}{2}\\\\y=2~~~~~~~~~~S=(x=8;~~y=2)$

$c)~metodo~da~adicao~(multipique~a~segunda~equacao~por~2\\\\~~~~~~~~~~-2x-~6y=~~6\\~+~~~~~~~~~2x+14y=-6\\~~~~~~~~~~---------\\~~~~~~~~~~~~~~~0+~8y~=~~0\\\\8y=0\\\\y=0\\\\substitua~(y=0)~em~uma~das~equacoes:\\\\x+7y=-3\\\\x+7.0=-3\\\\x+0=-3\\\\x=-3~~~~~~~~~~S=(y=0;~~x=-3)$

$d)~metodo~da~adicao~(multiplique~a~primeira~equacao~por~(-3)\\\\~~~~~~~~~~~-15x+3y=-3\\~~+~~~~~~~~~~2x-3y=~10\\~~~~~~~~~~~~--------\\~~~~~~~~~~~~-13x+0=~~7\\\\-13x=7\\\\x=-\frac{13}{7}\\\\substitua~(x=-\frac{13}{7})~em~uma~das~equacoes:\\\\2x-3y=10\\\\2~.~(-\frac{13}{7})-3y=10\\\\-3y=10+\frac{26}{7}\\\\mmc=7\\\\-3y=\frac{70+26}{7}\\ \\ -3y=\frac{96}{7}\\\\-y=\frac{96}{3.7}=\frac{96}{21}\\\\-y=\frac{32}{7}\\\\y=-\frac{32}{7}~~~~~~~~~~~S=(x=-\frac{13}{7};~~y=-\frac{32}{7})$

$e)~metodo~da~adicao~(multiplique~a~primeira~equacao~por~(-2)\\\\~~~~~~~~~~-2x-16y=28\\~+~~~~~~~~~2x-~3y=-3\\~~~~~~-----------\\~~~~~~~~~~~~~~~~0-19y=25\\\\-19y=25\\\\19y=-25\\\\y=-\frac{25}{19}\\\\substitua~(y=-\frac{25}{19})~em~uma~das~equacoes:~$

$2x-3y=-3\\\\2x-(-\frac{25}{19})=-3\\\\2x+\frac{25}{19}=-3\\\\2x=-3-\frac{25}{19}\\\\x=2(-3-\frac{25}{19})\\\\x=-6-\frac{50}{19}\\\\mmc=19\\\\x=\frac{-114-50}{19}\\\\x=-\frac{164}{19}~~~~~~~~~~S=(x=-\frac{164}{19};~~y=-\frac{25}{19})$