Question

1 - Encontre os valores de X, Y, Z.

a) {x + y - z = 4
{2y + z = 10
{3z = 15

b) {x + y + z = 0
{ y - z = 5
{ 2z = 8

c) {4x + y + 2z = -1
{ 5y - z = 0
{ z = -5

d) {2x + y - z = 8
{ 2y + z = 0
{ 2z = 4

e) {x + y + z = 8
{ y - z = 2
{ 4z = 2​

Answer 1

Resposta:

a) X = -7/2  Y = 5/2  Z =5

b) X = -13 Y = 9  Z = 4

c) X = 5/2  Y = -1  Z = -5

d) X = 11/2  Y = -1 Z = 2

e) X = 7  Y =  1/2 Z = 1/12

Explicação passo a passo:

a) X = -7/2  Y = 5/2  Z =5

I - 3z = 15

z = 15/3

z = 5

II - 2y + 5 = 10

2y = 10 - 5

y = 5 /2

III - x +  5/2 + 5 = 4

$\frac{2x + 5 + 10}{2} = \frac{8}{2}$

2x + 5 + 10 = 8

2x + 15 = 8

2x = - 7

x = -7/2

b) X = -13 Y = 9  Z = 4

I - 2z = 8

z = 8/2

z = 4

II - Y - 4 = 5

Y - 4 = 5

Y = 5 + 4

Y = 9

III - x+ y + z = 0

X + 9 + 4 = 0

X + 13 = 0

X = -13

c) X = 5/2  Y = -1  Z = -5

I - z = -5

II - 5y - z = 0

5y - (-5) = 0

5y + 5 = 0

5y = - 5

y = -1

III - 4x + y + 2z = -1

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

4x - 1 - 10 = -1

4x = 10

x = 5/2

d) X = 11/2  Y = -1 Z = 2

I - 2z = 4

z= 4 /2

z = 2

II  - 2y + 2 = 0

2y = - 2

y = -2/2

y = - 1

III - 2x + y - z = 8

2x - 1 - 2 = 8

2x - 3 = 8

2x = 11

x = 11/2

e) X = 7  Y =  1/2 Z = 1/12

I - 4z = 2

z = 2/4

z = 1/2

II - y - 1/2 = 0

y = 1/2

III - x + y + z = 8

x + 1/2 + 1/2 = 8

x + 1 = 8

x = 7

Espero ter ajudado :)

Bons Estudos!