Question

resolva os sistemas de equações: a) { x= 5y , x+ y =18 b) { x= 9y , x+3y= 24 c) { 2x + y = 5 , 5x- y = 2 d) { x-y = 8 , 2x+ 4y = 28 e) x+ 2y = 12 , 2x + 2y = 16 . eeeee urgente e para hoje por favor alguem me ajuda

Answer 1

$a)\\ \\ x=5y\\ x+y=18\\ \\Substitua~(x=5y)~em~(x+y=18)\\ \\ 5y+y=18\\ \\ 6y=18\\ \\ y=\frac{18}{6} \\ \\ y=3\\ \\ Substitua~(y=3)~em~(x=5y)\\ \\ x=5.3\\ \\ x=15~~~~~~~~~~S=(x=15;~~y=3)$

$b)\\ \\ x=9y\\ x+3y=24\\ \\ Substitua~(x=9y)~em~(x+3y=24)\\ \\ 9y+3y=24\\ \\ 12y=24\\ \\ y=\frac{24}{12} \\ \\ y=2\\ \\ Substitua~(y=2)~em~(x=9y)\\ \\ x=9.2\\ \\ x=18~~~~~~~~~~~~~~~S=(x=18;~~y=2)$

$c)~metodo~da~adicao:some~as~equacoes\\ \\ ~~~~~~~~2x+y=5~...........~equacao~I\\ ~+~~~5x-y=2~.........~equacao~II\\ ~~~~~~~-----\\ ~~~~~~~7x+0=7\\ \\ 7x=7\\ \\ x=\frac{7}{7} \\ \\ x=1\\ \\ Substitua~(x=1)~em~uma~das~equacoes:\\ \\ 2x+y=5\\ \\ 2.1+y=5\\ \\ 2+y=5\\ \\ y=5-2\\ \\ y=3~~~~~~~~~~~~~S=(x=1;~~y=3)$

$d)~metodo~da~substituicao:\\ \\ x-y=8~............~equacao~I\\ 2x+4y=28~.....~equacao~II\\ \\ Na~equacao~I:\\ \\ x=8+y\\ \\ Substitua~(x=8+y)~na~equaqcao~II\\ \\ 2x+4y=28\\ \\ 2(8+y)+4y=28\\ \\ 16+2y+4y=28\\ \\ 6y=28-16\\ \\ 6y=12\\ \\ y=\frac{12}{6} \\ \\ y=2\\ \\ Substitua~(y=2)~na~equacao~I\\ \\ x-y=8\\ \\ x-2=8\\ \\ x=8+2\\ \\ x=10~~~~~~~~~~S=(x=10;~~y=2)$

$e)~metodo~da~adicao:multiplique~a~equacao~I~por~(-2)\\ \\ x+2y=12~.........~equacao~I~.~(-2)\\ \\ ~~~~~~-2x-4y=-24~.....~equacao~I\\ ~+~~~~~2x+2y=~~16~.....equacao~II~~~~~~~some~as~equacoes\\ ~~~~~~~~------\\ ~~~~~~~~~~~0-2y=-8\\ \\ -2y=-8(-1)\\ \\ 2y=8\\ \\ y=\frac{8}{2} \\ \\ y=4\\ \\ substitua~(y=4)~em~uma~das~equacoes:\\ \\ x+2y=12\\ \\ x+2.4=12\\ \\ x+8=12\\ \\ x=12-8\\ \\ x=4~~~~~~~~S=(x=4;~~y=4;~~x=y)$