Question

Question #513a8

Answer 1

solve for t in the 3 equations with t:
`x=3+2t`
`(x-3)/2=t`

`y=6+t`
`y-6=t`

`z=4+3t`
`(z-4)/3=t`

set the t's equal to each other:
`(x-3)/2 = y-6 = (z-4)/3` (this is the condensed equation for the line)

do the same for s:
`x = −1 + 4s`
`(x+1)/4=s`

`y = 4 + 2s`
`(y-4)/2=s`

`z = −2 + 6s`
`(z+2)/6=s`

`(x+1)/4 = (y-4)/2 = (z+2)/6`
multiply all 3 sides by 2: `(x+1)/2 = y-4 = (z+2)/3`
subtract all 3 sides by 2: `(x-3)/2 = y-6 = (z-4)/3`

the 2 equations are the same so it's the same line