{x+4y-z=3
{x+5y-2z=5
{3x+12y-3z=9
possible answers:
x = 3z + 5, and y = z - 2, where z is any real number
or {(x, y, z) |x = 3z + 5, and y = z - 2, where z is any real number}

x = z - 2, and y = -3z - 5, where z is any real number
or {(x, y, z) |x = z - 2, and y = -3z - 5, where z is any real number}

x = -3z - 5, and y = z + 2, where z is any real number
or {(x, y, z) |x = -3z - 5, and y = z + 2, where z is any real number}

inconsistent

Question

{x+4y-z=3
{x+5y-2z=5
{3x+12y-3z=9
possible answers:
x = 3z + 5, and y = z - 2, where z is any real number
or {(x, y, z) |x = 3z + 5, and y = z - 2, where z is any real number}
		
x = z - 2, and y = -3z - 5, where z is any real number
or {(x, y, z) |x = z - 2, and y = -3z - 5, where z is any real number}
		
x = -3z - 5, and y = z + 2, where z is any real number
or {(x, y, z) |x = -3z - 5, and y = z + 2, where z is any real number}
		
inconsistent

mertsj · Answer

-2x-8y+2z=-6
x+5y-2x=5
Adding:  -x-3y=-1

mertsj · Answer

-3x-12y+3z=-9
3x+12y-3z=9
0=0

anonymous · Answer

so whats the answer ? you are telling me that this is dependent?

mertsj · Answer

x=-3z-5
y=z+2

mertsj · Answer

The third choice.

anonymous · Answer

thank you sir I really appreciate it

mertsj · Answer

yw