Please help me understand....?

2x-y+z=-3 AND 2x+2y+3z=2 AND 3x-3y-z=-4

(3, 5)

(-1, 7)

No Solutions

Infinitely Many Solutions

Question

Please help me understand....?

2x-y+z=-3  AND   2x+2y+3z=2   AND   3x-3y-z=-4

(3, 5)
		
(-1, 7)
		
No Solutions
		
Infinitely Many Solutions

anonymous · Answer

Here's some music to enjoy while working through the problem: http://www.youtube.com/watch?v=SIocOsmM0kg

anonymous · Answer

Basically all three of those equations are planes in 3 dimensions. 

If the three planes never cross paths there are no solutions. this is the case if they are all parallel (think about two lines, if they never cross in 2 dimensions they must be parallel.

anonymous · Answer

So there is no solution?

anonymous · Answer

OH!!!!!!!!!!!! Infinite ones?!!!

anonymous · Answer

Because it's never ending.....

anonymous · Answer

if two are parallel and one is not then there are infinitely many

is this linear algebra or calc 3?

anonymous · Answer

Algebra

anonymous · Answer

Oh my god, thank you so much. It seemed so obvious....!

anonymous · Answer

u can also just set up a matrix |dw:1349719415315:dw|

anonymous · Answer

You're right....I should've thought of that....!

anonymous · Answer

Can you help me again?

anonymous · Answer

so, what we are trying to solve is Ax=b, solve for x where A is our matrix above and b is the extra column at the end

anonymous · Answer

if we can turn A into the Identity martix, the answers will appear in front of us

anonymous · Answer

Thank you kind Greg

anonymous · Answer

I understand now

anonymous · Answer

I've done A LOT of work on my own, but I NEED to make sure I'm correct

anonymous · Answer

subtracting for 1 from row 2 is a step in the right directions|dw:1349719804429:dw|