When doing this kind of problem, we're going to look at our variables and we want to find some that are positive and some that are negative, and if possible with one coefficients. So when I look at this, I'm going to get rid of the TS because I have a negative TA, positive T, and another positive TI. Would highly recommend labeling your equations as 1-2 and three so that when you're keeping track, you can see what you're doing. We're going to combine one and two together. To start, if I combine one and two, I get 2R minus three s -, t equaling -8, and I get 2R plus 5S plus T equaling 6. So when I add these, the negative T and positive T are going to cancel, and we get 4R plus 2S equal -2 Now, I encourage keeping the number small so we can actually see that all of this is divisible by A2SO2R plus S equal -1 Let's call this our equation 4. Now we're going to go back to the first three equations. We've used 1:00 and 2:00, so we absolutely now have to use three, but we can decide whether we want to use one or two. With three, I'm going to use one because here's a positive T and there's a negative T. So if I use one and three, 2R minus three s -, t equal -8 when I add those, the TS cancel and we get three r -, 4 S equal -7. This is my equation 5. So if we write those next to each other, two r + s equal -1 and three r -, 4 S equal -7. Now this turns into a problem similar to Section 3. Two, we're going to get rid of the s s this time because I can multiply the top one just three by a four. We could get rid of the Rs, but I'd have to multiply the top by three and the bottom by two because we need additive inverses. So this case I can just multiply that top one by four and get 8R plus 4S equal -4 and three r -, 4 S equal -7. So we get 11 R equaling -11 or R equal -1. Once we get R, we have to plug it back into four or five in order to get S, and it doesn't matter which one I'm going to do 4, so 2R plus S equal -1. But we just found R was -1, so we're going to get -2 + S equal -1 or S equal 1. Now once we have R&S, we can put it into any of the original 312 or three to get RT so -1 -, 1 + t equal 1, so -2 + t equal 1, T equal 3. So our ordered triplet is going to be -1, then one and then three.