solve-each-system-of-equations-beginarrayrxyz9-yz7-z4endarray

Question

Solve each system of equations.
$$\begin{array}{r}x+y+z=9 \y+z=7 \z=4\end{array}$$

Jake Zanazzi · Accepted Answer

so here, actually, given a system equations in three variables last to solve exports. Wife was the equals nine. Why plus Z equals seven and Z equals four. So you think substitution is the same as we did with two variables we&#x27;re solving for one of the variables and we have to plug in to solve through the other ones. So here you&#x27;re given that Z equals four. So it&#x27;s easy to substitute that into the second equation. Do you have? Why cross four equal seven. Therefore, wives equal three. Now you&#x27;ve y goes three z equals four. You use those to solve for acts, scenario eggs plus three cross for equals nine and executed equal to now we have our answer actually close to what was three z equals four. You can write that as X comma. Why Z equals 234

Jake Zanazzi · Answer

All right. So you were given our system of equations with experts cycles for why minus equals Negative two X plus y plus equals, not way actually solve this problem using substitution. You can see that you have. Why all of these equations so you&#x27;re going to do is we can solve for acts in terms of why didn&#x27;t solve for Z in terms of why plug these all in and then actually solve for why? And then work backwards to solve for accent See. So let&#x27;s do that. Um, using his first equation, that X is gonna equal four minus y in the second equation waken get that Z equals. Why close to you do that? You just move this negative to over to this side move busy over the side. So then, if we go, this last equation were needed before minus Why that people to act Plus why, plus why plus two equals nine. This is gonna simplify these you&#x27;re gonna cancel. This is gonna turn into six. When you subtract that, you&#x27;re gonna get lie close. Three on your bike was three. We know that X equals four minus. Why so executed one d is gonna equal Y plus two z is getting equal five. So I have to go back to double check that these answers make sense. X plus y it&#x27;s one plus three equals four. Why? Minus Z three minus five equals negative too. And if you some all of these, you&#x27;re gonna it not So now we have or order trip All destroyed. It is this equals one comma. Three comma thought yes.

Ashley Volpe · Answer

start with the first and second equations. So I have X minus two uh, plus three Z equals one and negative two x plus seven, while modest non Z equals four. I noticed the last equation has X&#x27;s and Z&#x27;s in it. So I&#x27;m gonna eliminate my wise to do that. I&#x27;m gonna most by the top equation by seven on the bottom equation by two to make my walk. Hornets have the same coefficient. So that&#x27;s then going to give me seven x minus 14. Why? Plus 21 C able seven and negative for X Plus 14. Why minus 18 z equals eight. Now the wise have the same coordinates, so I can add to get three x plus three. Zine I was 15. This is a seven. It was 15 now at Third Equation had X&#x27;s and Z&#x27;s in it. And if you remember, that equation was X plus Z equals none. And so if I want to match it up with this equation, let&#x27;s multiply by three before we put it down there. And if we do that, we&#x27;re gonna get three X plus three z equals 27. When we subtract that we get zero equal to negative 12 which we know can&#x27;t happen, and we have no solution to this system

Jake Zanazzi · Answer

all right. Something use, uh, elimination to solve this system of equations. So we have a two x year in a two x year so we can eliminate X in these first do grazes by adding them. That&#x27;s gonna give you this equation right here. And from there you can solve for y and say that Y equals one minus c. If you multiply this second equation by two, you&#x27;re gonna get two X minus two y plus four z equals negative 10. And if you subtract his first equation minus the second equation, you&#x27;ll be left with negative Y minus three Z equals one. If you use this Y equals one minus Z, you&#x27;re gonna get negative One. Plus, is he minus three Z equals one, which means you&#x27;re gonna get negative two d equals two and therefore because he equals negative one. Well, it&#x27;s just that will take an X sense. Negative one minus one is negative to minus three times active one that equals one. So that checks out. Once we have Z, we can put back and get why, um, y is one minus e. So why is gonna equal to that? We could put back into this equation or here in sulphur acts. Are they gonna give us X minus two minus two equals negative five. Uh, which is gonna give us X minus four equals negative five. If you add four, you get X equals Negative one. Now we have order. Triple X Y Z equals negative one to negative one. Even double check that this works are you take you times. Negative one. Subtract six. It&#x27;s negative. Eight plus and plus the negative one. That&#x27;s 99 the other two equations will hold as well. So you have your answer.

Himanshu Kushwaha · Answer

have given two X plus y plus there is equal to nine minus X minus y plus there is equal to one and three x minus y plus Jared is equal to nine. Let&#x27;s say this is a Christian one. This is a prison to end. This is it. Isn&#x27;t V a reason? One With vision three. V Get five x plus through there is 1/4 to 18 Now the big vision. The air crescent first with exorcism Second vigor X plus through there is a world pen We subjected toe vig, ETF or X is equal to aid. It implies that X is equal to to now replace s accident Will goto in prison for Viggen through there is equal toe 18 minus 10. This is equal to eight we get There is a world for very place X equal Toto and jet is equal before in existence. Second figure minus two minus y plus four is equal to one. It implies that y is equal toe to minus one. This it equal woven so vigorous. Y is a world of on this story are the service and off the system

Jake Zanazzi · Answer

it&#x27;s here again. Assist on the X plus y. We&#x27;ll see people&#x27;s no actress plus why equals five and Z one. So here were given one. C equals so we could actually plug us into this first equation, um, and then see if we can solve it. So we&#x27;re gonna have X plus y plus point equals nine or expose wide equals Pete. But now we see that we have actual asswipe will survive and X plus y equals speak. And we know that this could never be the case You can ever have an excellent why that equals five and eat. So we know that there&#x27;s no solution for this system of equity.

Problem

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

Problem 7 Easy Difficulty

Solve each system of equations.
$$\begin{array}{r}x+y+z=9 \\y+z=7 \\z=4\end{array}$$

Answer

$\{(2,3,4)\}$

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Video Transcript

Mark Dugopolski

Algebra for College Students

Lily A.

Grace H.

Boris M.

Shubham P.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

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$\{(2,3,4)\}$

Algebra for College Students

Lily A.

Grace H.

Boris M.

Shubham P.

Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

Mark DugopolskiAlgebra for College Students

Lily A.

Grace H.

Boris M.

Shubham P.

Mark Dugopolski

Algebra for College Students