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.