Question

resolva os sistemas abaixo relacionados​

Answer 1

Resposta:

$a)~~substituicao\\ \\ x-3y=9~~equacao~I\\ 2x+3y=6~~equacao~II\\ \\ na~equacao~I\\ \\ x=9+3y\\ \\ substitua~o~valor~de~x~na~equacao~II\\ \\ equacao~II\\ \\ 2x+3y=6\\ \\ 2(9+3y)+3y=6\\ \\ 18+6y+3y=6\\ \\ 6y+3y=6-18\\ \\ 9y=-12\\ \\ y=-\frac{12}{9} =-\frac{4}{3} \\ \\ na~equacao~I\\ \\ x-3y=9\\ \\ x-3(-\frac{4}{3} )=9\\ \\ x+\frac{12}{3} =9\\ \\ x+4=9\\ \\ x=9-4\\ \\ x=5\\ \\S \left \{ {{5,~~-\frac{4}{3} } {} \}$

$b)~~adicao~(multiplique~a~equacao~II~por~-1)\\ \\ ~~~~~~2x+y=-3\\ +~-x-y=~1\\ ~~~~-------\\ ~~~~~~x+0=-2\\ \\ x=-2\\ \\ substitua~(x=-2)~em~uma~das~equacoes\\ \\ x+y=-1\\ \\ -2+y=-1\\ \\ y=-1+2\\ \\ y=1\\ \\ S~~\left \{ {{-2,~~1} {}} \}$

$c)~~substituicao\\ \\ x=3y~~(substitua)\\ \\ 2(3y)-4y=6\\ \\ 6y-4y=6\\ \\ 2y=6\\ \\ y=\frac{6}{2} =3\\ \\ x=3y\\ \\ x=3.3\\ \\ x=9\\ \\ S~~\left \{ {{9,~~3} {}} \}$

$d)~~comparacao\\ \\ equacao~I:\\ \\ 3x+2y=5\\ \\ 3x=5-2y\\ \\ x=\frac{5-2y}{3} \\ \\ Equacao~II\\ \\ 5x-3y=2\\ \\ 5x=2+3y\\ \\ x=\frac{2+3y}{5} \\ \\ x=x,~logo:\\ \\ \frac{5-2y}{3} =\frac{2+3y}{5} ~~(multiplique~em~cruz)\\ \\ 3(2+3y)=5(5-2y)\\ \\ 6+9y=25-10y\\ \\ 9y+10y=25-6\\ \\ 19y=19\\ \\ y=\frac{19}{19} =1\\ \\ substitua~(y=1)~em~uma~das~equacoes\\ \\ 3x+2y=5\\ \\ 3x+2.1=5\\ \\ 3x+2=5\\ \\ 3x=5-2\\ \\ 3x=3\\ \\ x=\frac{3}{3} =1$

$S~~\left \{ {{x=y=1} {}} \}$

$e)~~substituicao\\ \\ substitua~(x=-5y)~na~outra~equacao\\ \\ 4x-y=-21\\ \\ 4(-5y)-y=-21\\ \\ -20y-y=-21\\ \\ -21y=-21\\ \\ y=\frac{-21}{-21} \\ \\ y=1\\ \\ substitua~y~na~equaqcao~I\\ \\ x=-5y\\ \\ x=-5.1\\ \\ x=-5\\ \\S \left \{ {{-5,~~1} {}} \}$