Find solutions using elementary row operations

x+2y+z=0

2x+5y+2x=0

x+4y+7z=0

x+3y+3z=0

I subtracted 2 times the 1st equation from the 2nd to get y=0 and I subtracted the 4th eq from equation 3 to get y+4z=0, so z also equals 0. X would also equal 0, but did I do enough steps to qualify for elementray row operations? I don't want to lose points because I missed steps.