solve following system of linear equations by using simplex

2x+y-z=1

-2x+2y-z=-2

x+z=3

x,y,z>=0

here no objective fn is given i tried to use artificial variables and make a auxilarly lpp but this is not also working as i am getting a solution that satisfies only the first and second equations i.e. i am getting the values of only x and z

please help..