Are these planes parallel and distinct or parallel and coincident ? 3x+9y-6z-24=0 4x+6y-14z-8=0

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Are these planes parallel and distinct or parallel and coincident ? 3x+9y-6z-24=0 4x+6y-14z-8=0

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Divide the first by 3 and the second by 2, for starters.
@tkhunny and then ??
What do you get?

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Other answers:

x=4+5z
?? What is that? I was hoping you would get: x+3y-2z-8=0 2x+3y-7z-4=0
Yes i did
Then i did elimination to get rid of y
Why? Are they parallel?
Yes
We have to figure of if theyre parallel and distinct or coincidentt
They are? What makes you think so? When you eliminated y, didn't that give you a line in the x-z plane?
its given in the question
Are you going to buy it, just because it says so? If they are parallel, shouldn't they have the same Normal Vector?
so they're not parallel, they intersect ?
That's what they look like to me.
Answer key says parallel and coincident
3x+9y-6z-24=0 4x+6y-14z-8=0 Find a point on one of them. (10,0,1) Prove 3(10) + 9(0) - 6(1) - 24 = 30 + 0 - 6 - 24 = 24 - 24 = 0 Is it on the other one? 4(10) + 6(0) - 14(1) - 8 = 40 - 14 - 8 = 26 - 8 = 18 \(\ne 0\) Okay, we just proved that they are NOT coincident. Did you write the problem correctly? If you did, we're done.

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