Okay so i've spent a good amount of time between yesterday evening and today trying to figure out how to solve this problem using cramer's rule:

x + y +z = 0

7x- y +z=-10

-x+ 4y-z=-20

I heard that Cramer's rule isn't the best way to do this with this many equations and the simple add, substitution and elimination way would be somewhat better but even that way i've gotten the wrong solution. I've tried to eliminate X first by multiplying the first equation by -7 to get -8y-6z=-10 and then i changed the thrid equation to get 27y-6z=-150. I can't remember my exact answer because i erased the rest of it but i solved for z first once i combined them and got a small number and after i finished back substitution everything else i got 2 big numbers that didn't come out as the solution to each of the three equation. I was wondering if anyone could make it clear to me how i should go about solving this problem. Thanks.