Show that there does not exist x,y,z

[rooski]

Homework Statement

Show that there does not exist integers x,y,z such that

2x + 4y === 1 (mod 7)
x + y + 4z === 2 (mod 7)
y + 3z === 3 (mod 7)

The Attempt at a Solution

Should i be using substitution or elimination to solve this?

I could do something like

2x + 4y + 0z
x + y + 4z
_________
x + 3y - 4z


Or am i going in the wrong direction?

 

[tiny-tim]

hi rooski!

hint: try adding the second and third equations

 

[Outlined]

Another suggestion, work in the field F₇ (in fact you do but, someway not really -> anyway, forget about the mod 7 and keep in mind it is F₇ which behaves like R)

After that you can just do linear algebra (you probably already learned for R and C) to finish your question