Consider the following system of three equations:
3x+5y+6z=0
x+y+4z=0
3x+3y+12z=0
this system has no solution, infinitely many solution, a unique solution
x+y+4z=0
3x+3y+12z=0
these are the same equation, the second is the first times 3. You have two equations and three unknowns
X could be anything, pick 0
5 y + 6 z = 0
1 y + 4 z = 0
3 y + 12 z = 0 same as above
So x could be anything at all and we could still find a y and z