




Suppose the row reduced form of your equations are
x, y, z; c
0, 1, 3; 2
1, 0, 1; 1
Then z is a basis variable; the general solution to this pair of equations is
y = 2  3z, x = 1 + z, and of course z = z.
Remember that moving terms to the other side of the equation changes signs. You can eliminate z to get y = 1  3x if you like.