Respuestas

2012-08-16T15:13:10+02:00
Relative value of z:
x + 4y + 2z = 0
2z = - x - 4y
z = - 1/2x - 2y

Relative value of y (substitute z):
3x - 2y + 7z = 0
3x - 2y + 7(- 1/2x - 2y) = 0
3x - 2y - 7/2x - 14y = 0
16y = 6/2x - 7/2x
16y = - 1/2x
y = - 1/32x

Relative value of z (substitute y):
z = - 1/2x - 2(- 1/32x)
z = - 1/2 + 1/16x
z = - 8/16 + 1/16x
z = - 7/16x

Value of x (substitute y and z):
2x - (-1/32x) + 4(- 7/16x) = 15
2x + 1/32x - 28/16 = 15
64/32x + 1/32x - 56/32x = 15
9/32x = 15
x = 160/3

Value of y (substitute x):
= - 1/32(160/3)
= - 5/3

Value of z (substitute x):
= - 7/16(160/3)
= - 70/3

Answer: x = 160/3, y = - 5/3, z = - 70/3

Proofs of the three original equations:
160/3 + 4(- 5/3) + 2(- 70/3) = 0
160/3 - 20/3 - 140/3 = 0

3(160/3) - 2(- 5/3) + 7(- 70/3) = 0
480/3 + 10/3 - 490/3 = 0

2(160/3) - (- 5/3) + 4(- 70/3) = 15
320/3 + 5/3 - 280/3 = 15
45/3 = 15
15 = 15