Maths help please!! the question is:?

Question

Maths help please!! the question is:?

find a set of parametric equations for the line in 3 space described by the general equations x-y-z=4 and x+y-5z = 12

thanku very much

Answer 1

Let z be the free parameter (denoted by t), then z=t

x-y-t=4...(1)

x+y-5t=12...(2)

(2)-(1): 2y-4t=8 => y=2t+4

(1)+(2): 2x-6t=16 => x=3t+8

Answer 2

You have given us two equations of planes:

x - y - z = 4

x + y - 5z = 12

When these planes intersect, they will do so at a line. We will solve this using matrices (ignore the dots):

| 1 -1 -1 | 4.. |

| 1 .1 -5 | 12 |.....R2 → R2 - R1

| 1 -1 -1 | 4 |

| 0 .2 -4 | 8 |

Let z = t:

2y - 4t = 8

2y = 8 + 4t

y = 4 + 2t

x - y - z = 4

x - (4 + 2t) - t = 4

x = 4 + t + (4 + 2t)

x = 8 + 3t

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Your parametric equations are:

x = 8 + 3t

y = 4 + 2t

z = t