Question

determine as soluções dos sistemas abaixo mentalmente e registre-as. a)x+y=10 x-y=6 b)x+y=7 x-y=3 c)x+y=12 x/y=2 d)y=2x x-y=0

Answer 1

$a)\\ \\ ~~~~ ~~~x+y=10~~~~~equacao~I\\ +~~~x-y=~6~~~~~~ equacao~II~~~~~(metodo~da~adicao)\\ ~~~~------\\ ~~~~~2x+0=16\\ \\ 2x=16\\ \\ x=\frac{16}{2} \\ \\ x=8\\ \\ substitua~(x=8)~em~uma~das~equacoes:\\ \\ x+y=10~~~~~~equacao~I\\ \\ 8+y=10\\ \\ y=10-8\\ \\ y=2\\ \\ S=(x=8,~~y=2)$

$b)\\ \\ ~~~~~~~~x+y=7~~~equacao~I\\ +~~~~x-y=3~~~equacao~II~(metodo~da~adicao)\\ ~~~~~------\\ ~~~~~2x+0=10\\ \\ 2x=10\\ \\ x=\frac{10}{2} \\ \\ x=5\\ \\ substitua~(x=5)~em~uma~das~equacoes:\\ \\ x+y=7~~~equacao~I\\ \\ 5+y=7\\ \\ y=7-5\\ \\ y=2\\ \\ S=(x=5,~~y=2)$

$c)\\ \\ x+y=12~~~~~~equacao~I\\ \\ \frac{x}{y} =2\\ \\ x=2y~~~equacao~II\\\\metodo~da~substituicao\\\\substitua~(x=2y)~na~equacao~I\\ \\ x+y=12~~~~~equacao~I\\ \\ 2y+ y=12\\ \\ 3y=12\\ \\ y=\frac{12}{3} \\ \\ y=4\\ \\ substitua~(y=4)~em~uma~das~equacoes:\\ \\ x=2y~~~equacao~II\\ \\ x=2.4\\ \\ x=8\\ \\ S=(x=8,~y=4)$

$d)\\ \\ y=2x~~~~~~~~~equacao~I\\ \\ x-y=0~~~~~equacaoII\\ \\ substitua~(y=2x)~na~equacao~II\\ \\ x-y=0~~~~~~equacao~II\\ \\ x-2x=0\\ \\ -x=0\\ \\ x=0\\ \\ substitua~(x=0)~em~uma~das~equacoes:\\ \\ y=2x~~~equacao~I\\ \\ y=2.0\\ \\ y=0\\ \\ S=(x=0,~~y=0)~~~~(x=y=0)$