When solving systems of 3 equations & 3 unknowns..... If they all cancel does that mean is No Solution?

Question

unklerhaukus · Answer

for example

x=x
y=y
z=z

there are three fold infinite solutions

anonymous · Answer

Ok.  I'm confused

unklerhaukus · Answer

no solutions occur when the equations dont make sense

x=1
y=2
x+y=0

has zero solutions

anonymous · Answer

the problem is: 4x +2y+6z=13, -12x+3y-5z=8, -4x+7y+7z=34.  When I put two equations together to eliminate 1 variable.  My results end up the same for Eq4 & 5 which then cancel each other.  Ex.  -9y-13z=-47 
                            9y+13z=47

anonymous · Answer

Oh.  Ok so since it all cancels.  Then the answer is infinite solution?

unklerhaukus · Answer

4x +2y+6z=13,   i
-12x+3y-5z=8,   ii
-4x+7y+7z=34,  iii

9y+13z=47         i+iii

anonymous · Answer

I got what you were trying to explain.  It's infinite solution because 0=0 which mean it is dependent

unklerhaukus · Answer

how did you get to 0=0?

anonymous · Answer

The all cancel out so variables are 0 and = 0

anonymous · Answer

I did it on my paper.  I had to multiply Eq 4 by -1 to utilize elimination method and 4 and 5 cancel out

unklerhaukus · Answer

4x +2y+6z=13,   i
-12x+3y-5z=8,   ii

9y+13z=47          ii+3i

unklerhaukus · Answer

i+iii    -   ii+3i

0x+0y+0z=0

all values of x,y,z satisfy this equation

anonymous · Answer

so the answer is dependent

anonymous · Answer

infinite solutions

unklerhaukus · Answer

if you graph the three plains , you will find that they look something like this 

|dw:1350781829769:dw|

the intersection is a infinite line of solutions