Question

a) {x+y+2=0
{x-y-4=0

b) {3x+y=7
{2x-y=8

c) {x=2y
{2x+3y=4

d) {x-2y=3
{x+y= -4

e) {2x+y=1
{x-y= -4

f) {x=5
{x+y=7

g) {-2x+y=5
{x-y= -1

h) {y= - radical 2 x
{x- radical 2 y = 3

i) {x supra 3 = y supra 1
{10x -3y = -1

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

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Answer 1

Răspuns:

a)

x + y = -2 => x = -2 - y

x - y = 4

-2 - y - y = 4

-2y = 6

y = -3

x = -2 + 3

x = 1

b)

3x + y = 7 => y = 7 - 3x

2x - y = 8

2x - (7 - 3x) = 8

2x - 7 + 3x = 8

5x = 8 + 7

5x = 15

x = 3

y = 7 - 3(3)

y = 7 - 9

y = - 2

c)

x = 2y

2x + 3y = 4

2(2y) + 3y = 4

4y + 3y = 4

7y = 4

y = 4/7

x = 2(4/7)

x = 8/7

d)

x - 2y = 3 => x = 3 + 2y

x + y = - 4

3 + 2y + y = -4

3y = -4 - 3

3y = -7

y = -7/3

x = 3 + 2(-7/3)

x = 3 - 14/3

e)

2x + y = 1 => y = 1 - 2x

x - y = -4

x - (1 - 2x) = -4

x - 1 + 2x = -4

3x = -4 + 1

3x = -3

x = -1

y = 1 - 2(-1)

y = 1 + 2

y = 3

f)

x = 5

x + y = 7

5 + y = 7

y = 7 - 5

y = 2

g)

-2x + y = 5

x - y = -1 => x + 1 = y

-2x + x + 1 = 5

-x = 5 - 1

-x = 4

x = -4

i)

$\frac{x}{3} = \frac{y}{1}$

x = 3y

10x - 3y = -1

10(3y) - 3y = -1

30y - 3y = -1

27y = -1

y = -1/27

x = 3(-1/27)

x = -1/9

j)

y = 3x

2x + y = 3

2x + 3x = 3

5x = 3

x = 3/5

y = 3(3/5)

y = 9/5