Question

Resolva os seguintes sistemas. A) {-×+2y= -3 ·····{5x-2y= -1 B){2x-y=3 ····{x+y=3 C){×+2y=8 ····{2x-y=6 D){q-p=6 ····{q+p=12

Answer 1

Método de adição

A)

{-x+2y= -3
{5x-2y= -1
----------------
4x = -4
x = -4/4
x = -1

Valor de y:

5x - 2y = -1
5 . (-1) -2y = -1
-5 - 2y = -1
-2y = -1 + 5
-2y = 4
y = 4/(-2)
y = -2

B)

{2x-y=3
{x+y=3
-------------
3x = 6
x = 6/3
x = 2

Valor de y:

x + y = 3
2 + y = 3
y = 3 - 2
y = 1

C)

{x+2y=8
{2x-y=6 . 2

#########

x + 2y = 8
4x - 2y = 12
------------------
5x = 20
x = 20/5
x = 4

Valor de y:

x + 2y = 8
4 + 2y = 8
2y = 8 - 4
2y = 4
y = 4/2
y = 2

D)

{q-p=6
{q+p=12
-------------
2q = 18
q = 18/2
q = 9

Valor de y:

q + p = 12
9 + p = 12
p = 12-9
p = 3

Answer 2

Resolva os seguintes sistemas.

A)

{-×+2y= -3
{5x-2y= -1

{x=3+2y
{5x-2y= -1

5 (3+2y)-2y= -1
15+10y-2y= -1
10y-2y= -1 -15
8y= -16
y= -2

5x-2*(-2)= -1
5x+4= -1
5x= -1-4
x= -5/5=> -1


B)

{2x-y=3
{x+y=3

{x=3+y/2
{x-y=3

3+y/2+y =3

y=1


x+1=3
x=3-1
x=2

C)


{×+2y=8
{2x-y=6

{x=8-2y
{2x-y=6

2 (8--2y)-y=6
y=2

2x-2=6
x=4



D)

{q-p=6
{q+p=12

{q=6+p
{q+p=12

6+p+p=12

p=3

q+3=12

q=9