State why the system of equationsmust have at least one solution

Question

anonymous · Answer

attachment

anonymous · Answer

Compute the rank of the augmented matrix and then ...

anonymous · Answer

no they dont want me to do that

anonymous · Answer

They want to say a reason y it has at least one solution from just looking at the set of equations

anonymous · Answer

Aw yes, it's a homogeneous system so  there is always the  trivial solution which is $  x=y=z=0$.

anonymous · Answer

huh?

anonymous · Answer

that isnt covered in this unit

anonymous · Answer

That is a correct solution and probably the one they should ask for.

anonymous · Answer

no i dont think that is what they are looking for

anonymous · Answer

Good luck then :-)

anonymous · Answer

LOL Thanks

mertsj · Answer

Because the first equation is a line and it will intersect the other two.

anonymous · Answer

i can say why in english

anonymous · Answer

huh?

anonymous · Answer

not sure it will help, but the first equation is a line, and you can solve for y in terms of x.  then you will have two equations in two unknowns (the bottom two) and so long as they are not parallel there will be a solution

jamesj · Answer

Even if you haven't discussed homogenous systems yet, it's obvious that 
x=y=z=0 
is a solution.

jamesj · Answer

...hence the system has at least one solution.

anonymous · Answer

Well i kind of have a feeling that it has to do with that every equation =0

jamesj · Answer

There's all kind of theory around this.  

But if the question is just 
"State why the system of equationsmust have at least one solution"

then the fact that 
x=y=z=0 is a solution 

is a sufficient reason.

anonymous · Answer

K thanks :DDDD

anonymous · Answer

OHHH now i get it. It was so obvious LOL