solve-each-system-beginalignedxy-z2xyz8xy-z6endaligned

Question

Solve each system.
$$\begin{aligned}&x+y-z=2\&x+y+z=8\&x+y-z=6\end{aligned}$$

Jake Zanazzi · Accepted Answer

it&#x27;s a theory of X plus. Why, minus he was too explosive. Y plus z equal eat and X plus y minus Z equals six. We even notice here. Is these the first equation here in this third equation have the same exact left side, right? It&#x27;s X plus Y minus Z, except for the equal. Two different numbers. We know this can never be the case. They&#x27;re never You could never have a combination of x, y and Z that equal to different numbers. That doesn&#x27;t make any sense, right? Because what happens is if you set these equations equal to each other, right, you&#x27;ve X y z X y z you&#x27;re gonna get to equal six, which obviously does make sense.

Elisa Ma · Answer

in this problem, we&#x27;re going to solve this system of equations. But first we need to see if there&#x27;s going to be a unique solution to see if there&#x27;s a unique solution. The determinant off this on Matrix should not be zero. So this is the co efficient matrix, and we need to find a determine off this. So we will separate this by Rowing Column to find the Matrix or to find the determinant. So this equals one times the determinant of 48 Negative one negative too minus one times 36 Negative one negative too, plus or minus one times 3648 So we get one times four times negative to minus eight times negative one minus one times three times Negative to minus six times negative one minus one times three times eight minus six times For we get one times negative eight plus eight minus one times negative six plus six minus one times 24 minus 24. One times zero minus one time. Zero minus one time zero This is all zero. So that means there is no unique solution

Grace Muhihu · Answer

Okay, So for this problem, what we&#x27;re gonna do first is we&#x27;re gonna solve. Why? Using the first equation. So with that will have that Y is equal to two acts, plus c posture. Okay, so from there, we can go ahead and plug this why? Into the second and third equation in frizzy. So what that will have So we plug into the second equation will have X minus three times. Why? Which is this right here? Two x plus C plus two. And this is gonna be equal to negative two. Okay, so we simplify. This will have X minus six X minus three. Z minus six is equal to negative two. So now we, um ca minus have the X is on this side and the Z on the side, and then we bring our constance to the right. Will have to x minus three. Z e is equal to positive for. Okay, so this will be our equation that we will get later. So now we want to plug Z or we want to plug. Why? Into our third equation. So what? That will have six x minus two times two acts plus seeing plus two plus three z is equal to negative for So we just plugged. Why? Into the third equation. So here I&#x27;m just going to simplify a little bit. So what? That&#x27;ll have six x minus or X minus two Z minus for plus three Z is equal to negative, for If I simplify this, I combined these exes and I combined these choose ease and bring this constant of the side. I&#x27;ll have the following in creation of two x plus C is equal to zero. Okay, so I&#x27;m gonna now look at this equation as well. So when I look at my two underlined equations ones that are underlined in red So from here, I&#x27;m gonna line them up, so I&#x27;m gonna have to x minus three Z is equal to four and two x plus C is equal to zero. So I just took these two equations. Now I want to eliminate us. I want to eliminate X. In this case, I&#x27;m gonna multiply this whole equation by negative one. So with that, I will have the following two equations will have two X minus three Z is equal to four as my first equation, and then I&#x27;ll have negative two x minus Z is equal to zero. So if I lined these up, these will drop out and I&#x27;ll have negative for Z is equal to positive force it just add these going down divide both sides, but negative for and I will get that Z is equal to negative one. So it&#x27;s gonna be 1/3 of my solution. So now I have to go and solve, um ex and why So with that I can use these two equations that I have either one of these equations that I have up here. So I&#x27;m going to use this one right here. Two x plus c to solve, uh, X. So what? That&#x27;ll have to X plus C. But Z is negative. One so minus one is equal to zero. So not going to solve X here. So I add want to both sides now have to acts is ableto one. So that means X is equal to 1/2. Okay, so we have our second solution. And now if we go back to that equation we had in the beginning where why is equal to two x plus C plus two. So if we do that we will have. So why is equal Teoh? So why is going to be equal to two acts and X is 1/2 and then plus C which is negative born and then plus two. So with that, if we simplify that we get that why is able to positive too? These are gonna be our three solutions for this problem.

Jake Zanazzi · Answer

Alright, sums come right out our system here we We have a system of equations on their number of ways. You can solve this. Um, what I&#x27;m gonna do first is solve for X in terms of Z plugged that into this equation and then used those two equations to solve for y and Z doing this is gonna give us X equals Z minus e. And then I&#x27;m gonna plug right into two Z minus feet minus Why? It was negative feet, right? Because I&#x27;m clinging this you&#x27;re into this equation right here is gonna give us to the minus 16 minus why equals negative, eat or choose a modest why he pulls eat. But now it&#x27;s a to Z minus. Live was a and y plus three z equals 22. What we What we could do is we can manipulate this equation to say why equals two z minus e and plug that into this equation right here. So we have to z minus B plus three z was 22 is gonna go five z equals 30. He&#x27;s gonna equal six. Want to know that g of six We can play that back into this equation? right here I get Why equals four once we know it&#x27;s here. Six and wise four. We know X equals E minus eight. So acts is gonna equal negative, too. Now we have. Our answer is you can plug lives back in.

Adam Dehollander · Answer

in this part, we see that we can solve to get why in terms of sea and we can start to get excellent terms at sea and said that if we do that, we can like everything into the top equation and get in it Asian on Lee in terms of C. So let&#x27;s do that. That&#x27;s first so far. Why in our second equation? So if we add, see over six to both sides and then what about a boy that would give us why? Is equal to 2/3 I&#x27;m see? And now in our that equation, if we add Zito both sides and then divide by two that gives us the axe is equal to connected to divide back to its nectar one. And then we have passed of Shia Divide by two another. Which one is she? And so now we have X and y in terms of sea, so it&#x27;s like that into a tap equation. So six times acts is six. I&#x27;m snake. Give one us 1/2. See, that&#x27;s why just to see minus four C is equal connective. So that&#x27;s combine that Z terms. We have a 1/2 see Time&#x27;s a 60 is who we see. And then if we subtract, it was easy. That is negative one. See, we still have a tooth. Didn&#x27;t see right here. And then with that Constance, we have a negative six on this side. So when we add that to the right side of the equation, that leaves us with negative too. And so now if we do a negative Z 1st 2/3 E, that leaves us a negative one thingy. It&#x27;s equal connective too. And if we want both sides of the equation by negative three and gives us then CIA secret sex And so now we have one of the variable soft boy we can plug that into this equation to Third Z is equal to why two things Time six we can do six divided by three is two times two. So why a secret for? And then we just have one more beer but herself for that specs. So we see that the excess negative one plus 1/2 see so that 1/2 see is 1/2 time sex with three D Answer three plus negative one. It&#x27;s true. Xs equal to high secret of four and CIA secrets

Himanshu Kushwaha · Answer

18 x minus three by plus six There is equal to minus two four X plus in nine by plus four. There is word 18 12 X minus three. Why? Plus here too there is equal to minus two letter. This is a Christian one. This is a crescent toe and this is a crescent. Three women reply exists and one Valtteri, we get 24 x minus nine. Vying plus 18. Gerard is equal to minus six. Now, if we air ECW isn&#x27;t for with vision to, then we get 28 banks plus 18 plus for eight minutes 22 there is equal to 18 minus six. That is equally true. Well, this gives us for being X plus 11. There it&#x27;s 1/4 to 6 now, if you multiply it. Prison three by three we get 36 X minus nine y plus 20 for Jerry is equal to minus six. Elected. This is a prison five. Now the air present five and prison toe. We get four p X plus 28. There is equal group. This implies that 20 X plus four mean there is equal toe six. Now if we simplify deeds toe crescents for X and Gen then vigor. The value off X is equal toe minus terry, divided by four. And if they replaced the value off eggs in any equation from these two, then vigor the value off Gerry and the barely off is equal to three. Divide by two. The place the value of X there in any off first to the equals and we get Y is equal to five, divided by three. So this this and this is the sort of person off the given system.

Problem

Solve each system. $$\begin{aligned}x+y+z &=6 \\2…

Problem 29 Easy Difficulty

Solve each system.
$$\begin{aligned}&x+y-z=2\\&x+y+z=8\\&x+y-z=6\end{aligned}$$

Answer

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