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Problem 48

For the following exercises, solve the system for $x, y,$ and $z$

$$

\begin{array}{l}{\frac{x+4}{7}-\frac{y-1}{6}+\frac{z+2}{3}=1} \\ {\frac{x-2}{4}+\frac{y+1}{8}-\frac{z+8}{12}=0} \\ {\frac{x+6}{3}-\frac{y+2}{3}+\frac{z+4}{2}=3}\end{array}

$$

Answer

When solving the equations using elimination method or addition method, the result obtained is an identity, $0=0,$ which tells us that this system has an infinite number of solutions.

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## Discussion

## Video Transcript

All right. So question number 48 I'm trying to make things again. The extension section Trying to make things a little bit more difficult. Unlike the last problem where we had the same denominated in problem. This time we have different denominators problem. And so we need to find the number that 76 and three we'll all go into evenly. Okay. Um, that would be 42 something. You All right? So what? End up getting ISS six times X plus four gave it seven. We're going do the 42 6 times six goes in the 47 times minus seven times why minus one and then three goes in tow 40 to 14 times. Okay, so we end up getting plus 40. Arms equals two equals 42. Oh, just made it. Okay, next one number that 48 12 All going to evenly. Um, you see? So cycle need 83 24. Just one baby. So for rosen, 24 6 times six ex moments, too. Eight balls in 24 3 times. Plus three. Why this one? And then 1200 for two times. Minus to Z A equals zero times. Anything is zero last equation I removed by this equation by six tons of pollution by six. So he goes in 62 times two, six, and then three guards in the 60 times. So minus two. Why? It looks too. And then, um, two years in the 63 times three z equals three times six. A lot of work just to get started. We haven't really You've got going on the solving of the thing yet, so be patient here. All right. Um, I don't need to distribute on the top here, so get six X plus 24 minus seven. Why? Plus seven plus support to Z. Um, close. 28 peoples. Were you two? Hey, um, get this in our standard warm for these sorts of problems, we have six X minus seven. What us or to Z equals form 42 two. He's 24. My seven minus 20 years. This negative 17 here. All right, now, next one. Same idea. Six X minus 12. Plus the why was three minus two z minus its team zero Put it in good form here. So it sits X plus three. Why minus two z equals Oh, three. 25. All right, now, finally, the last one. Yeah. To axe most 12 minus two. Why? Minus four to my mother's. For just easy. I was 12 was 18. Two acts minus two. What? Plus three z equals you, too. There's 12. It's war. It's 12 again Two. Okay. Oh, okay. So I'm gonna take this last equation. Um, I'm gonna multiply this by three. Six x minus sense. Why? Plus mine Z equals negative six. Right? And then let me see. Talk to equations. Let's subtract those. Okay? Yeah. So, six months. 603 miles. Not your seven. It's 10 Y, uh, negative to minus 49. 16 z equals 25 minus negative. 17. 25. US 17 which is 42. I'll take the Eastern equations and will subtract them. Let's go down. Yeah. So three minus negative. Six is three plus. It's It's 91 And then, um, negative to minus 9 11 See, Equals 25 miles in eight. Year 36. 31. Looks like be animal by this morning. Well, Rick is down for a second here. Wait. 10 War minus 16. Two. My Why? Minus 11. Z equals 31. Start that on on a new age. So he was where we are, right? 10 1 My 16 years e he was 42. In On what? It's 11 instead of one. All right. Said by this equation by nine this equation by 10. So 90 Why? Minus wondered for before Z equals 42 times nine. 370. I'm sorry. 3 78 Yeah. And this becomes 91 minus 110. Z equals 310. And then we're going to subtract these two equations on Let's attract them. So negative. 1 10 my snagged 1 44 is plus 1 34 34 z equals 3 10 My side is negative. 68. Bye bye. 34. See? Negative too. Now they got Z was negative to go back in in these equations and do this one nine. Why? Minus 11 times Maybe That too, equals 31. It's mine. Why? Plus 22 people's 31 right? So that means nine X equals nine and X equals one. All right, then defined. Um I just had actually said this is all Why? Why now? To find X and go back to the first age find a good equation to work with. Um, how about to exports to I plus two. B z two two X minus two X minus two. Why two ex minds too? Trust me, Z was negative too. Waas really see equals negative too. Okay, so two X minus two minus six. His name, too sounds to X. People's six. It's at eight. Tip to both sides. So that means x waas three. And it was my answer. Order triple three two.

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