Question

1- Determine o conjunto solução de cada um dos sistemas abaixo:
a){
x + y = 7
x − y = 5

b){
x + y = 40
x − y = 8

c){
4x − 2y = 6
x + y = 9

d){
x + 2y = 7
x − y = −2

e){
x + y = 110
x − y = 30 f){

3x + 2y = 10
x + y = 4

g){
3x + 2y = 5
5x − 3y = 2

h){
4x + 3y = 5
2x − 5y = 9

i){
3x + y = 19
x + y = 7

j){
x + y = 26
2x + 3y = 68

Answer 1

Resposta:

$a)~metodo~da~adicao\\ \\ ~~~~~~~~x+y=7\\ +~~~~x-y=5\\ ~~~~~~------\\ ~~~~~~~2x+0=12\\ \\ 2x=12\\ \\ x=\frac{12}{2} \\ \\ x=6\\ \\substitua~(x=6)~em~uma~das~equacoes\\ \\ x+y=7\\ \\ 6+y=7\\ \\ y=7-6\\ \\ y=1\\ \\ S~\left \{ {{x=6;~~y=1} {}} \}$

$b)~metodo~da~adicao\\ \\ ~~~~~~~~x+y=40\\ +~~~~x-y=8\\ ~~~~~~------\\ ~~~~~~2x+0=48\\ \\ 2x=48\\ \\ x=\frac{48}{2} \\ \\ x=24\\ \\ substitua~(x=24)~em~uma~das~equacoes\\ \\x+y=40\\ \\ 24+y=40\\ \\ y=40-24\\ \\ y=16\\ \\ S~\left \{ {{x=24;~~y=16} {}} \}$

$c)~metodo~da~substituicao\\ \\ 4x-2y=6~...~equacao~I\\ \\ x+y=9~...~equaqcao~II\\ \\ na~equacao~II\\ \\ x+y=9\\ \\ x=9-y\\ \\ substitua~(x=y-9)~na~equacao~I\\ \\ equacao~I\\ \\ 4x-2y=6\\ \\ 4(y-9)-2y=6\\ \\ 4y-36-2y=6\\ \\ 4y-2y=6+36\\ \\ 2y=42\\ \\ y=\frac{42}{2} \\ \\ y=21\\ \\ substitua~(y=21)~em~uma~das~equacoes\\ \\ na~equacao~II\\ \\ x+y=9\\ \\ x+21=9\\ \\ x=9-21\\ \\ x=-12\\ \\ S~\left \{ {{y=21;~~x=-12} {}} \}$

$d)~metodo~da~adicao~[multiplique~uma~equacao~por~(-1)]\\ \\ equacao~I\\ \\ x+2y=7~.(-1)\\ \\ ~~~~~~~~-x-2y=-7~...~equacao~I\\ +~~~~~~~~x-~y=-2\\~~~~~~~~~-------\\ ~~~~~~~~0-3y=-9\\ \\ -3y=-9\\ \\ y=\frac{-9}{-3} \\ \\ y=+3\\ \\ substitua~(y=3)~em~uma~das~equacoes\\ \\ x-y=-2\\ \\ x-3=-2\\ \\ x=-2+3\\ \\ x=1\\ \\ S~\left \{ {{x=1;~~y=3} {}} \}$