When doing this problem, we need to figure out whether we want to get rid of X's, YS or Z's. The rule of thumb is we want some that are positive and negative and we want some that have one coefficients. Well, we don't have any variable that has one coefficients and positive as negatives. So when I look at this, I'm going to do Z because the numbers are relatively small. I have going to have to multiply by a negative and that's OK. I once again recommend labeling them as 1-2 and three before we get started. If I'm going to get rid of the ZS, I need to have additive inverses, so I'm going to multiply this top equation through by a -2 so I get -10 X -6 Y -2 Z equal -48. So this is combining one and two. I had to multiply this number 1 by -2 so X -, 3 Y +2 Z equal -15. When I add those together, I can see I get -9 X -9 Y equaling. The Z's will cancel and we get 33. Now I always, always, oh wait, those are both negatives. So that's not really what we get. Eight and five is 363, negative 63. I always try to keep these numbers as small as possible. So I'm going to divide through by a -9 and I'm going to get X + y = 7 and that's going to be my new equation 4. Now I have to use equation 3, and this time I'm going to use one because if I take equation 1 and multiply it by -3, I can make those Z's cancel. So one and three, where I'm going to multiply 1 by -3 so -15 X -9 Y -3 Z equaling -72 negative 3 * 24. And then we're going to leave the equation 3 alone. And when I add these, we can see the ZS are going to cancel again. It's important that we cancel the same variable and we're going to get -67 So that's my equation 5. Now I'm going to take four and five together, and if I look at 4:00 and 5:00 the way they are, the X's will cancel if I just add the two because they're already additive inverses. So I get -10 Y equaling -60 or y = 6. Once I get the Y equal, I'm going to substitute back into four or five in order to get the X. So I'm going to put it in four and I'm going to get X + 6 = 7, so X equal 1. Once I have my X and my Yi can put it into any of the three original, I'm going to use one. So 5 * 1 + 3 * 6 + Z equal 24. So 5 + 18 + Z equal 24. So 23 + Z is 24, so Z equal 1. So our ordered triplets going to be 1-6 and one for the system.