Question

D) 2x+y=5
x-y=4
E)2x+3y=8
x-2y=4
F)x+y=5
-x+y=3
G)3x+y=4
-x+y=4
encontrar o valor do x e do y

Answer 1

Resposta:

Sistemas de equações do primeiro grau

$D)\\ \\ metodo~da~adicao:\\ \\ ~~~~~~2x+y=5~~equacao~I\\ +~~~x-y=4~~equacao~II\\ ~~~------\\ ~~~~~3x+0=9\\ \\ 3x=9\\ \\ x=\frac{9}{3} =3\\ \\ substitua~(x=3)~em~uma~das~equacoes\\ \\ equacao~~I\\ \\ 2x+y=5\\ \\ 2.3+y=5\\ \\ 6+y=5\\ \\ y=5-6=-1\\ \\ x=3;~~y=-1$

$E)\\ \\ Metodo~da~substituicao\\ \\ 2x+3y=8~~equacao~I\\ x-2y=4~~~equacao~II\\ \\ na~equacao~II\\ \\ x-2y=4\\ \\ x=4+2y\\ \\ substitua~(x=4+2y)~na~equacao~I\\ \\ equacao~I\\ \\ 2x+3y=8\\ \\ 2.(4+2y)+3y=8\\ \\ 8+4y+3y=8\\ \\ 4y+3y=8-8\\ \\ 7y=0\\ \\ y=\frac{0}{7} =0\\ \\ substitua~(y=0)~em~uma~das~equacoes\\ \\ equacao~II\\ \\ x-2y=4\\ \\ x-2.0=4\\ \\ x-0=4\\ \\ x=4;~~y=0$

$F)\\ \\ metodo~da~adicao\\ \\ ~~~~~~~~~~x+y=5~~equacao~I\\ +~~-x+y=3~~equacao~II\\~~~~~~~~------\\ ~~~~~~~~0+2y=8\\ \\ 2y=8\\ \\ y=\frac{8}{2} =4\\ \\ substitua~(y=4)~em~uma~das~equacoes\\ \\ equacao~I\\ \\ x+y=5\\ \\ x+4=5\\ \\ x=5-4\\ \\ x=1;~~y=4$

$G)\\ \\ metodo~da~adicao\\ multiplique~uma~das~equacoes~por~(-1)~para~anular~o~valor~de~y:\\ \\ -x+y=4~.(-1)=x-y=-4\\ \\ ~~~~~~~~~~3x+y=~~4~~equacao~I\\ +~~~~~~~~x-y=-4~~equacao~~II\\ ~~~~~~~~~~------\\ ~~~~~~~~~~4x+0=0\\ \\ 4x=0\\ \\ x=\frac{0}{4} =0\\ \\ substitua~(x=0)~em~uma~das~equacoes\\ \\ equacao~I\\ \\ 3x+y=4\\ \\ 3.0+y=4\\ \\ 0+y=4\\ \\ y=4\\ \\ x=0;~~y=4$