First of all we will eliminate x from our equations. In order to do that we will use our first and second equation and then we will use second and third equation.
Upon subtracting 2 equation from 1 we will get,
Now we will use second and third equation to eliminate x.
Adding 2nd and 3rd equation we will get,
Now we will find out y from our 4th and 5th equation.
Upon subtracting 5th equation from 4th equation we will get,
Now let us find out z by substituting y's value in 5th equation.
Now we will find x from by substituting y and z's value in equation 1.
Therefore, x=1, y=1 and z=0 is the solution of the given system.