solve-each-system-of-equations-beginaligned2-x-5-y2-z163-x2-y-3-z-194-x-3-y4-z18endaligned

Question

Solve each system of equations.

$$\begin{aligned}&2 x-5 y+2 z=16\&3 x+2 y-3 z=-19\&4 x-3 y+4 z=18\end{aligned}$$

Jake Zanazzi · Accepted Answer

All right, So you river system equations two X minus five y plus two z equals 16 three X plus two ah, minus three Z equals, like 19 and four X minus three y plus four z equals eight. What I noticed here is that we have a two X here in a four x A to Z and a four Z that looks like something we can eliminate and potentially solve for y. In one step, we multiply this rest equation by two. I&#x27;m gonna give us four X minus 10. Why? Plus four z equals 32. Now, if we subtract this first equation and the spirit equation, remember you left with four X minus four Ex Your ex Negative 10 wine minus negative. Three wide negative seven. Why four Z minus four Z zero now 30 to minus 18 is 14. This king of this? Why equals negative too. Now, this problem came a lot easier. Um, because we have three equations and only two unknowns we can plug in this wide was negative two, um, to really any of these equations we plug in a negative to here and get plus can, um and then this will turn into a six that if we plug when I give you in here, we&#x27;re gonna This is gonna become a, uh, minus four, which is gonna turn into if you add affordable sides. Um, this is gonna become negative 15. Now, we can use these two equations to solve for Z and X. If you divide every term in here about two, you&#x27;re gonna have X plus Z equals three. From there, you can save a, uh, ex equals three minus. Is he just going toe? Move our work down here. Right now, we have three acts which we nose three times three minus E minus three. Z equals negative 15. Most part that out earlier. Nine by 60 people&#x27;s negative. 15 subtracted nine. And that&#x27;s gonna be negative. 24 which is gonna give you Z was 412 years equals four. You know that ax equals negative one. So now we have our order Triple X Y Z schools. Give one from a negative two comma, fourth and double check By putting those in to make sure makes sense, remember to plug them into the initial equations. Not just this to expose to Z and three X minus three Z. You want to make sure that the Y coordinate except

Jake Zanazzi · Answer

All right. So you&#x27;re giving in Equation three x four. Why c equals 19 two x those four y z zero and X minus two y plus five p equals writing. All right, Sorry. 17. So I see a to To To out here for why here in a four y here. Something we can use elimination and eliminate. Why? So if we add these 1st 2 operations together, five acts zero Why A to Z equals night kids. And now, if you multiply the start equation by two, that&#x27;s gonna leave us with. So it&#x27;s gonna be, um we&#x27;re gonna have to subtract. So it&#x27;s gonna be three x minus three x zero x negative for Why mine those. I were most finance by two because we want the four wide four wives to cancel. So it&#x27;s gonna be three x minus two x Just gonna be X negative. Four y minus Negative. Two y zero Z minus 10 Z B minus nine. Z equals 19 minus 34. Which is gonna be negative. 15. All right, so now we can solve for X and Z, right? We have X equals knives e plus 15 so we can put bread and up here to get five, five times 90 plus 15 lost. Uzi Legal 19. This is gonna give us 45 Z plus 15 times five 45 Z plus 75 45 p plus 75 close to Z. So it&#x27;s gonna be 40. 70 equals 1975. It&#x27;s gonna be negative. 56. You see, here we get a really weird number which tells us that we probably made him steak earlier on, and it turns out we did. Um, this nine z, it&#x27;s gonna be a minus here now, plus right. So that&#x27;s gonna change things. We have 90 minus 15 Now, this is gonna give us 45 acts minus 75 plus two to, um, sorry. This should be easy crossed. Uzi People&#x27;s 19 on this is gonna give us 75 plus 19 94 divided by 47. This is gonna give us C equals two, which makes a lot more sense once we have the equals two. We complain that in and we get X equals three. And now we just plugged back in and salt for a while to use the second equation. Since I like that zero there. Two x six plus four. Why? Plus Z plus two equals zero on before you get four y equals negativity or why equals negative to Now we have our order. Triple X Y Z equals three comma. Negative. Two comma. Two. You could double check. This solution works. Remember? Like we ran into a little mistake and we got number. That really didn&#x27;t make sense. Um, it&#x27;s not likely they would give us that. We&#x27;re stranger. A fraction as an answer. So you go back, retrace your steps. Syrian steak is, um and then you end up at the sluice.

Ankit Gupta · Answer

So we have been given a set off equations as X plus three y plus five is equals to 20. And why minus was there is a close to minus 16. Three ex miners to why bless 90? Is it close to 36? So now we will name this the questions as one do on three. So first we will my reply minus three in question one Onda id with the question Todd. So therefore, we will get minus three X minus nine way minus 15 is that is equals to minus 60 three x minus. Do I plus lines owed is equals to 36. So minus 11. Why minus cigs There is it closed toe whiteness 24 and we will name the cell question for so multiply 11 in a question, too, and ad with the question for So therefore we&#x27;ll get 11. Why, minus 44 said is because toe minus 1 76 and here we have minus 11. Why minus six in is equals to minus during default. So therefore minus 50 zer is equals to minus 200 divided by four minus four on board that states so their physicals to so you divide by 50 minus 50 on board that say so we will have their physicals to four. Now we will substitute any question toe So any question to be f y minus for their physicals. Tu minus 16. So therefore why minus four multiplied with four is a close to minus 60. So therefore, why will be zero? No, we will substitute in equation one. Any question one is X plus three y plus five. There is equals to 20 x is unknown. Three month replied with zero plus five multiplied by four is opposed to 20 so x plus Wendy is equal to 20. So therefore X is also zero. So therefore you off x Goma Y, Toma said, is equal to zero coma, zero comma four

Tony Ni · Answer

locals, especially tonight. This question. You was on the system version using substitution so conceived from predatory that X is over. We have a professional wants all that you&#x27;ve done to our advantage by isolating next, so true will become that&#x27;s supposed to 21 6 Why plus eight By plugging into one. What we call get is about a local speciality night. This question was 21 6 Why us eight? As to why spend every single issue of Woods went fine menaced. Certainly. Why Plus 40 said, and as to why, Plus, and they collect on like that&#x27;s negative certain to why. Plus what industries only system person using substitution So they conceive front, predatory that X is over. We have a professional ones all that you&#x27;ve done to our advantage by isolating next, so true will become that&#x27;s supposed to 21 6 Why plus eight by plugging into one. Where we could get is a hey question and we&#x27;re gonna plug this well, we have over here into number two. That&#x27;s two 21 my six wide plus eight said minus Or why? What is that? Questioning that gives us 42 minus of why minus plus 16 21 6 wives Bus eight But it&#x27;s too. Why spend every scene? Bush ended Woods. One rope line menaced, Sir, The wine plus 40 said, That&#x27;s too Why plus 20 and then collect on like that&#x27;s negative. Certain to why. Plus for the mysteries minus four Wire. Linus, she said. Question negative. Nine. That this will. If we combine like term, we end up getting vigorous. 16. Why? Plus 13 close to No. One. And it&#x27;s called those version number four you question number. But okay, now we&#x27;re gonna see that ballsy question for a question. Then we&#x27;re gonna plug this. Well, we have over here into number two. That&#x27;s two 21. My six wide plus eight said minus. Or why? What is that? Questioning that gives us 42 minus. But why minus plus six things, no question about it. Hasn&#x27;t got a 16 white, which is half of it. The question for So let&#x27;s isolate the question. Number five 16 white They could, you know, if I become signature 16. Why? Because too negative 51 minus said chain. They plug that into number four. What can change? Never pour into bone number four was negative. Minus four wire. Linus, she said. Question negative. Nine. That this will. If we combine like term. We end up getting Nikolas 16. Why? Plus 13. Be close to one. And it&#x27;s called those question number four your question number. But okay, now we&#x27;re gonna see the post a question for you to why? Plus ordering story said D&#x27;Costa never. Maybe. Can&#x27;t be changing too. Negative. 16 Time. 16 wine times two plus, we&#x27;re going three zone. Most negative. Maybe I&#x27;m just being a certitude. Why is Think this is more times two. So that&#x27;s the same was right now. So we complete that in that snake and 51 minus. You haven&#x27;t got a 16 white, which is half of it. The question for So let&#x27;s isolate the question. Number five 16 white. They could, You know, if I become signature 16. Why? Because too negative. 51 minus searching. They plug that into number four. Why? Can change. Never pour into bone Number four was negative. 30 13 all times. Two us. What streets and question, *** ***. Really private expand. I should get negative 102 minus 26. Then he goes through. Plus 23 questions. And then you could come back to why. Plus ordering, sweetie, he said, Because you never know. Maybe five. Can&#x27;t be changing too. Negative. 16 Time 16 wine times two. Plus, we&#x27;re going three zone. Most negative. Maybe I&#x27;m just being a city to Why is Think this is more times two. So that&#x27;s the same was right now. So we complete that in that snake and 51 minus terms. I end up where? 17. In Khowst. You&#x27;re 17 Zen. Because 21 if I plug that into doing an original. If I plucked us into your question number five, I&#x27;m not sure that No, sir. I plugged this father. You between pleasure number five. We should end up with 16. Why? Because to negative 41 minus searching on that. Would you? Just 13. Because to me, of a 16. Why? Because Nicholas, 13. All times, two bus. What extremes and question? ***, ***. Really private expand. I should get a bigger 102 minus 26. Then he goes to us. Woody. Three questions. And then you had compounded. For what? Because to poor plugging boasts white. And was that on why? Value into numbers. You too Number. Story ended but was axe you because to 21 minus six times once 1/6 sense for us. Aten Jessa 800 won, which is 21 minus 20 or less bait which you can, too terms I end up where? 17. Close to 17. The Zen. Because 21 If I plug that into doing an original If I plug this into your question number five I&#x27;m not sure that No, sir. I plugged this father. You. Pleasure number five. This should end up with 16. Why? Because to make 41 minus 30. That would you? Just 13. Because to move a 16. Why? Because Nicholas, that&#x27;s our answer by for one.

Rebecca Polasek · Answer

I want to solve this system for X, Y and Z, that makes each of the equations true. So I&#x27;m looking for one of the variables that could cancel out. And I&#x27;m going to pick why as my very well, I want to eliminate. So to eliminate, why? I&#x27;m gonna focus first on equations one into on equation one. I actually know I&#x27;m going to change that because that&#x27;s where why is by itself already. So I want to keep equation to as is. So if I want to cancel out a negative two why, then I&#x27;m gonna need to have a plus two y above it. And to make a plus two y up there, I would have needed to multiply the entire equation times two So multiplying that entire first equation times too. I get four x plus two y minus four z equals negative 30. Now these two lines are ready to add Together I get eight x, the wise cancel out. We have negative three Z and then negative 15. I want to repeat that step and I want to cancel out the wise one more time so that I have another equation in just two variables that I can use to solve. And as I&#x27;m considering my equations, I think it looks easier to use equations one and three to make these wise match than it does to make equations two and three match. So when I focus on equations one and three, just like last time, I&#x27;m gonna leave Equation three as is because that&#x27;s already where I have the greater term for why and new I can make a match up here. I know I&#x27;m gonna be able to eliminate those wise because the television on the first line is just a one. So if I want to cancel the wise, I&#x27;m gonna need a negative three, which means I needed to multiply the entire first line times negative three. So negative six X positive 60 and then a positive 45. Bringing those lines together, we get a negative five x, the wise cancel out. We have eight Z and then 40. So now, on this part of the problem, I have two equations with just two variables to solve these. I&#x27;m gonna go ahead and use elimination again, and I&#x27;m gonna try and eliminate the ex term, which means I need to make eight X and negative five x cancel. Neither term can go into each other, right? Neither wants a factor there, so they&#x27;re gonna have to both multiply into the same number. And one of the easiest ways to do that is just multiply them together. Notice that both eight and five going to 40. That&#x27;s actually just eight times five. So a pretty easy way to make that elimination happen. It&#x27;s just multiply those coefficients together. So I&#x27;m gonna multiply times of five to the entire equation. It x minus three z equals negative. 15. I&#x27;m gonna use a positive five because I want to make sure that they cancel. So I do want them to have opposite signs there, and then I&#x27;m gonna multiply the second equation times eight. So I have a negative 40 axe plus 64 C equal to 3 20 And now, as I&#x27;m bringing these together, the 40 X is we&#x27;re gonna cancel out. I&#x27;m gonna have 49 z And then if I do negative 75 class 3 20 then I get to 45. So then to get Z by itself, I&#x27;ve seen to divide by 49 and 2 45 by by 49 is five So Z equals five. Now that I found my answer for See, I can feel this into either of my other equations to find an answer for X. I&#x27;m gonna go into the first equation. Replace that Z. So I have eight. X minus 15 equals negative 15. So to get exploit itself, you&#x27;re gonna have to add the 15 to the other side and then divide by eight. So we find that X equals zero. And then now that I have X and Z as answers, I can go into any of the three original equations to figure out my answer for why? So I&#x27;m just gonna fill into Equation one with X that I have and with the Z that I have these five fulfilling an X zero and then Z is five. I get why minus 10 equals negative 15. If I add that 10 over, I get, why is native five? So then the point that&#x27;s a solution for this system would be zero negative 55 and the X y Z

Rebecca Polasek · Answer

I went to solve system and I have three questions with three variables. So to solve the system, I probably want to try and eliminate one of the variables. So let&#x27;s try and get rid of X. If I want to eliminate X, maybe I use these 1st 2 equations together, but notice right now one X and two X don&#x27;t cancel out. So we&#x27;re gonna want to multiply this top equation by a negative too. So that way negative two x and positive two x Do eliminate each other. So multiplying the entire top equation by a negative two We get negative two x We get a positive for Why negative six z equals negative 10. And then I&#x27;m not going to change that second equation as I put these together. Negative two. X cancels two x well, negative for y cancels four way six cancels negative six z. Which leaves me a zero over here on the left side. But look at the right side. Negative. 10 and a three makes a negative seven. Does zero equal negative seven. No, this is a false statement. So because we ended up getting a statement that was false, like in this case zero equals negative seven. Then we say that the system is inconsistent and when the system is inconsistent, there is no solution. So if you end up with a false statement like zero equals 10 2 equals eight something that&#x27;s not true, then you say no solution.

Problem

Solve each system of equations. $$\begin{array}{…

Problem 21 Medium Difficulty

Solve each system of equations.

$$\begin{aligned}&2 x-5 y+2 z=16\\&3 x+2 y-3 z=-19\\&4 x-3 y+4 z=18\end{aligned}$$

Answer

$\{(-1,-2,4)\}$

Related Courses

Algebra for College Students

Related Topics

Discussion

Top Algebra 2 Educators

Grace H.

Ahyeon H.

Boris M.

Martha R.

Algebra 2 Courses

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Mark Dugopolski

Algebra for College Students

Grace H.

Ahyeon H.

Boris M.

Martha R.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\{(-1,-2,4)\}$

Algebra for College Students

Grace H.

Ahyeon H.

Boris M.

Martha R.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

Mark DugopolskiAlgebra for College Students

Grace H.

Ahyeon H.

Boris M.

Martha R.

Mark Dugopolski

Algebra for College Students