solve-each-system-of-equations-beginaligned2-x-y-8-y3-z-22-x-z-8endaligned

Question

Solve each system of equations.

$$\begin{aligned}2 x-y &=-8 \y+3 z &=22 \x-z &=-8\end{aligned}$$

Jake Zanazzi · Accepted 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.

Jake Zanazzi · Answer

So here we&#x27;re giving the system. When we&#x27;re told that two X equal seven was this means that access in the equal seven. About about two. Now, we can substitute that into this first equation to solve For why? So we&#x27;re gonna have seven over to miss Y equals three. So why is gonna equal three minus seven? Provided by two? Um, seven out of two is 3.5. So why&#x27;s unequal negative 0.5 now that we&#x27;ve wives insult Jersey, negative 0.5 plus Z equals eight Z is gonna equal 8.5. And we have, Excellency, that solves this system. It&#x27;s gonna be X Y Z equals, um seven forward to y&#x27;s negative one other two and z 17 over to.

Jake Zanazzi · 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.

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.

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.

Ankit Gupta · Answer

we have been given system of equations to so are small with equations, huh? Thanks Plus y minus eight is equal to eight X minus two y plus that is equal to three X plus three by because music is equal to seven we were leaving the question as a be I think we can see that our questions are already in the standard form. So no need to change now. The next step we will do is we will eliminate by variable from the question A and B on from equation. And okay, so I just take a question e that is X plus y mine instead is equal to eight. Any question be that the x minus. To my left, there is a girl to treat to eliminate by valuable we have to create equal and opposite condition. Don&#x27;t buy in both the equation Here we can see that it is minus two here displacement what we do. We were multiplied this equation by do and we&#x27;ll get Blix blessed to weigh minus two Said is equal to 16 Next, right as it is X minus two y plus that is equal to three. Adding wood The question we can see that minus two wind plus two way It can be eliminated. We will get three. X minus said is equal toe 19 named this beat. And now the data question eight that is X plus quite minor that execute toe eight. Any questions? See that X plus three by plus does that is equal toe seven. You&#x27;re also we will eliminate by so we can see that in this we have coefficient bloody And here it is plus one. So what we do, they will multiply it by mine. If three no, we will get minus T X minus three by blood. Three said is equal to minus 24. And the sea question they question, seek admitted. And as it did, that X plus three by plus two six is equal to seven. Now we will add Buday question. We can see that minor three million plus three. I can be eliminated. We will get minus two weeks plus fights that is equal to minus 17. Named this equation s e this s d right now, we will solve the question D and E to get the value of idol said or eat X No statistic in question be that if to the X minus fig, it&#x27;s equal to 19 minus two wigs plus five is equal to minus 17 we will eliminate anyone.

Problem

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

Problem 26 Medium Difficulty

Solve each system of equations.

$$\begin{aligned}2 x-y &=-8 \\y+3 z &=22 \\x-z &=-8\end{aligned}$$

Answer

$\{(-2,4,6)\}$

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Mark Dugopolski

Algebra for College Students

Lily A.

Boris M.

Shubham P.

Heather Z.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

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$\{(-2,4,6)\}$

Algebra for College Students

Lily A.

Boris M.

Shubham P.

Heather Z.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

Mark DugopolskiAlgebra for College Students

Lily A.

Boris M.

Shubham P.

Heather Z.

Mark Dugopolski

Algebra for College Students