So I have two equations that I\'m essentially doing the elimination method with:

Question

So I have two equations that I'm essentially doing the elimination method with:

9+6t=3+12s

+

12-3t=9-6s

I know this is basic math, but I've completley forgotten how to go about this. Both the t and s cancel each other out at the same time and so I've completely forgotten what to do when this happens. I'm using these two equations with a third one to determine whether a line is parallel, intersecting or skew. Heres the third just in case, 3+9t=12+15s

When both the t's and s's canceled out I figured that the line isn't intersecting and that it's skew. This was a hw problem and I got it correct. So I just want to verify that I'm going about this correctly since a problem similar to this will be appearing on my next exam. Any help is appreciated. Thank you.

Explanation / Answer

Yes, You are doing it correctly. So, s and t cancel each other means there doesn't exist any point at which these lines meet. Hence, Non-intersecting.

Now, Lets check if they are parallel.

A vector parallel to L1 is < 6,-3,9 > {coefficients of t }

A vector parallel to L2 is < 12,-6,15 > { coefficients of s }

Ratios of the first components = 6/12= 1/2

second= -3/-6= 1/2

third= 9/15 = 3/5

Hence, ratio is not same means they are not parallel.

So, They are Skew Lines.

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