Question

Sistemas de equação do 7o ano
1. Resolva o sistema usando a método da adição.
a, 4*+y=2 [ 3*+2y=7]

b, x-3y=1 2x+5y=13

c, 2x+y=10 x+3y=15

d, 3*+y=13 2*- y = 12

e, 2*+y=4 4*-3y=3

Answer 1

$4x+~y=2~.(-2)~multiplique~por~(-2)\\ \\ ~~~~~~~-8x-2y=-4\\ ~+~~~~~~3x+2y=~~7\\ ~~~~~~~~~~-------\\ ~~~~~~~-5x+~~0=~~3\\ \\ -5x=3\\ \\ x=-\frac{3}{5} \\ \\ Substitua~(x=-\frac{3}{5})~em~uma~das~equacoes\\ \\ 3x+2y=7\\ \\ 3.(-\frac{3}{5} )+2y=7\\ \\ -\frac{9}{5} +2y=7\\ \\ 2y=7-\frac{9}{5} \\\\mmc=5\\ \\ 2y=\frac{35-9}{5} \\ \\ 2y=\frac{26}{5} \\ \\ 5.2y=26\\ \\ 10y=26\\ \\ y=\frac{26}{10} =\frac{13}{5} \\ \\ S=(x=-\frac{3}{5} ,~~~y=\frac{13}{5} )$

$b)\\ \\ x-3y=1~.(-2)~multiplique por (-2)\\ \\ ~~~~~~-2x+6y=-2\\ ~+~~~~~2x+5y=~13\\ ~~~~~~~~-------\\ ~~~~~~~~~~0+11y=~11\\ \\ 11y=11\\ \\ y=\frac{11}{11} =1\\ \\ substitua~(y=1)]~em~uma~das~equacoes\\ \\ 2x+5y=13\\ \\ 2x+5.1=13\\ \\ 2x+5=13\\ \\ 2x=13-5\\ \\ 2x=8\\ \\ x=\frac{8}{2} \\ \\ x=4\\ \\ S=(x=4,~~y=1)$

$c)\\ \\ 2x+y=10~.(-3)~multiplique~por~(-3)\\ \\ ~~~~~~-6x-3y=-30\\ ~+~~~~~~~x+3y=~~15\\ ~~~~~~~~--------\\ ~~~~~~-5x+~~0=-15\\ \\ -5x=-15~(-1)\\ \\ 5x=15\\ \\ x=\frac{15}{5} \\ \\ x=3\\ \\ substitua~(x=3)~em~uma~das~equacoes\\ \\ x+3y=15\\ \\ 3+3y=15\\ \\ 3y=15-3\\ \\ 3y=12\\ \\ y=\frac{12}{3} \\ \\ y=4\\ \\ S=(x=3,~~y=4)$

$d)\\ \\ ~~~~~~~~~3x+y=13\\ ~+~~~~2x-y=12\\ ~~~~~-------\\ ~~~~~~~~~5x+0=25\\ \\ 5x=25\\ \\ x=\frac{25}{5} \\ \\ x=5\\ \\ substitua~(x=5)~em~uma~das~equacoes\\ \\ 3x+y=13\\ \\ 3.5+y=13\\ \\ 15+y=13\\ \\ y=13-15\\ \\ y=-2\\ \\ S=(x=5,~~y=-2)$

$e)\\ \\ 2x+y=4~.(-2)~multiplique~por~(-2)\\ \\ ~~~~~~-4x-2y=-8\\ ~+~~~~~4x-3y=~~3\\ ~~~~~~~~-------\\ 0-5y=-5\\ \\ -5y=-5~.(-1)\\ \\ 5y=5\\ \\ y=\frac{5}{5} =1\\ \\ substitua~(y=1)~em~uma~das~equacoes\\ \\ 2x+y=4\\ \\ 2x+1=4\\ \\ 2x=4-1\\ \\ 2x=3\\ \\ x=\frac{3}{2} \\ \\ S=x=\frac{3}{2} ,~~y=1)$

Answer 2

O que significa o "*" ?