Question

resolva os sistemas a){x+y =13 {4x-y=7 b) {x+y =-5 {-x+y=-6 c){-7x+y=-8 {7x-3y=-6 d){m+n=12 {3m-n=-4 e){-26x+3y=1 {+26x-2y=1 f){ -3x +4y= -20 {-3y-4y=+2​ AJUDEMMMMMM​

Answer 1

Resposta:

Método da adição

$a)\\ \\ ~~~~~~~~x+y=13\\ +~~~4x-y=~7\\ ~~~~~~------\\ ~~~~~~~~5x+0=20\\ \\ 5x=20\\ \\ x=\frac{20}{5}\\ \\ x=4\\ \\ x+y=13\\ \\ 4+y=13\\ \\ y=13-4\\ \\ y=9\\ \\ S\left \{ {{4;9} {}} \}$

$b)\\ \\ ~~~~~~~~x+y=~~~5\\ +~-x+y=-6\\ ~~~~~~~------\\ ~~~~~~~~0+2y=-1\\ \\ 2y=-1\\ \\ y=-\frac{1}{2}=-0,5 \\ \\ x+y=5\\ \\ x+(-\frac{1}{2} )=5\\ \\ x-\frac{1}{2} =5\\ \\ x=5+\frac{1}{2} \\ \\ x=\frac{10+1}{2} \\ \\ x=\frac{11}{2} =5,5\\ \\ S\left \{ {{-\frac{1}{2};\frac{11}{2} } } {}} \}$

$c)\\ \\ ~~~~~~~~-7x+y=-8\\ +~~~~~~~7x-3y=-6\\ ~~~~~~~~~~-------\\ ~~~~~~~~~~~~0-~2y=~~2\\ \\ -2y=2\\ \\ y=-\frac{2}{2} \\ \\ y=-1\\ \\ 7x-3y=-6\\ \\ 7x-3(-1)=-6\\ \\ 7x+3=-6\\ \\ 7x=-6-3\\ \\ 7x=-9\\ \\ x=-\frac{9}{7} \\ \\ S\left \{ {{-1;-\frac{9}{7} } {}} \}$

$d)\\ \\ ~~~~~~~~m+n=12\\ +~~~3m-n=-4\\ ~~~~~~-------\\ ~~~~~~~4m+0=~~8\\ \\ 4m=8\\ \\ m=\frac{8}{4} \\ \\ m=2\\ \\ m+n=12\\ \\ 4+n=12\\ \\ n=12-4\\ \\ n=8\\ \\ S\left \{ {{2;8} {}} \}$

$e)\\ \\ ~~~~~~~~~~~-26x~+3y=1\\ +~~~~~~~~~~~26x-~2y=1\\ ~~~~~~~~~~~~---------\\ ~~~~~~~~~~~~~~~~~0~~+~~y=1\\ \\ y=1\\ \\ 26x-2y=1\\ \\ 26x-2.1=1\\ \\ 26x-2=1\\ \\ 26x=1+2\\ \\ 26x=3\\ \\ x=\frac{3}{26} \\ \\ S\left \{ {{1;\frac{3}{26} } {}} \}$

$f)\\ \\~~~~~~~~~~ -3x+4y=-20\\ +~~~~~~-3x-4y=~~~~2\\ ~~~~~~~~~~--------\\~~~~~~~~~~ -6x+~~0=-18\\ \\ -6x=-18\\ \\ 6x=18\\ \\ x=\frac{18}{6} \\ \\ x=3\\ \\ -3x-4y=2\\ \\ -3.3-4y=2\\ \\ -9-4y=2\\ \\ -4y=2+9\\ \\ -4y=11\\ \\ y=-\frac{11}{4} \\ \\ S\left \{ {{3;-\frac{11}{4} } {}} \}$