Question

Resolva os sistemas abaixo o método da adição:

A) { x + y = 10
{ x - y = 3

B) { x + y = 7
{ 2x + y = 10

C) { x + y = -8
{ x - y = 2

D) { 3x + 2y = 17
{ 2x + y = 10

E) { 20x + 30y = 100
{ x + y = 4

Answer 1

A)
$\left \{ {{x+y=10} \atop {x-y=3}} \right.$
2x=13
x=6,5

x+y=10
6,5+y=10
y=10 - 6,5
y=3,5

B)
$\left \{ {{x + y = 7} \atop { 2x + y = 10}} \right.$ 
$\left \{ {{x+y=7 (-1)} \atop {2x + y = 10} \right.$
$\left \{ {{-x-y=-7} \atop {2x + y = 10}} \right.$
x=3

x+y=7
3+y=7
y=7 - 3
y=4

C)
$\left \{ {{ x + y = -8 } \atop { x - y = 2}} \right.$
2x=-6
x=-6/2
x=-3

x+y=-8
3+y=-8
y= -8 - 3
y= -11

D)
$\left \{ {{ 3x + 2y = 17} \atop {2x + y = 10}} \right.$
$\left \{ {{3x + 2y = 17} \atop {2x + y = 10 (-2)}} \right.$
$\left \{ {{3x + 2y = 17} \atop {-4x -2y = -20}} \right.$
-x=-3 (-1)
x=3

2x+y=10
2 · 3 + y = 10
6 + y = 10
y= 10 - 6
y = 4

E)
$\left \{ {{20x + 30y = 100} \atop {x + y = 4}} \right.$
$\left \{ {{20x + 30y = 100} \atop {x + y = 4 (-20)}} \right.$
$\left \{ {{20x + 30y = 100} \atop {-20x -20y = -80}} \right.$
10y=20
y=20/10
y=2

x + y = 4
x + 2 = 4
x = 4 - 2
x = 2