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Problem 12

For the following exercises, solve each system by substitution.

$$

\begin{aligned} 5 x-2 y+3 z &=20 \\ 2 x-4 y-3 z &=-9 \\ x+6 y-8 z &=21 \end{aligned}

$$

Answer

$x=4.9$

$y=4.58$

$z=1.43$

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## Discussion

## Video Transcript

All right, We're gonna solve this system of equations here by substitution. Okay, Um, why they pick substitution for this? I'm not really sure to be on speak. Um, but what you want to look for? What you gonna do? Substitution XYZ check out your equations and then figure out which of them is. He's just assault, variable. My vote goes for this last one because we already have X by itself. Okay, so I saw this equation for X. I'm gonna get X equals 21 minus its Why, plus eight z. Okay. And then I can take this value of X. And I can substitute that in or these exit first equation, the exit. The second equation. All right, so, um, let's do the first equation first. Okay, So ended. Getting the first equation. Five times 12 minus six. Why? Plus eight z. Some substituting my expression or X in four acts. But I still have the rest of this too. So admires, too. Why? Plus three z equals 20. Let's continue to simplify this before we get our next one that distracted. So five times 12. 16. All right, so and then we have minus 30 and then plus for Z and then minus two. Why plus three c. It was 20 that really careful as you do these not making silly little upstate somewhere on line. Hey, so, um, combining, like terms we see eye minutes attract. Well, see, talk about Silliman states. It just caught me. Okay, so I apologize for that, but I need to go back here, Um, a little dyslexia actually going here. That should have been 21. All right, so this should have been 21 which means that this year all right, this year, instead of being that again 7 21 here. So one of five. All right. So, um, do you think about that? It's not gonna come back to combine like, term move this. Subtract one of five from both sides. So I get negative. 85. We're here. They get their minds to is negative. 32. Why? And then 40 plus three is for free Z. Okay, that's pretty good right there. Um, not for my other equation. And I get the second equation. Substitute this for that also. So too times 21 minus six. Why? I'm bloody covens a Z and then I still got the minus for? Why? Modest? Easy equals native nine. Um, distribute 42 minus 12. Why? Plus 16 z minus for why minus three Z equals native nine. Okay, um, subtract 42 from both sides. So negative nine miles for you to use that one, um 12 y minds for why there's no. 16. What? Sorry, 16 one and then 16 Miles three is buster to Z. And now I need this soul, um, one of these equations for year y or Z. So that's all this one for? Why? So why would he Negative 51 minus 13 z over negative 16. Why did that with all the negatives? I don't know. But now I take this value. Um, just tell you why, and I'm gonna take that when substituted into the other equation. So I'm gonna get negative 32 times. Davis, you want minus 13 z were negative. 16 a plus 40 or C 43 you see, equals negative. Beautifies. All right, so moving right along. Um, this negative 16 goes in the negative 32 2 times and so that I may distribute that too. So I get negative 102 Um, minus 2060. Plus, we're greasy people's names. All right, so add 100 to so negative. 85 +102 It's me. In this case is 85 +12 iss 17 over here. All right. And then combine my disease. 43 minus 26 is 17. Yes, Team Z. Well, 17 z equals one. All right, So if Z was one now, I can find why using this equation here. So why's that being negative? 51 minus 13. Plans one over negative 16. Okay, which equals you. See, my restricting negative 16 is for, uh, feeling good. Now in whole numbers for answers. Okay. So for And then finally find X that I'm glad he's found that here. Um, X equals 21 minus six times war plus eight times. One big balls. You see, 21 minus 24 plus a She did a taxi. So my order triple it solves this. All right, so x comes first. Why? On second he comes third, there's your answer.