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Solve each system of equations.

$$\begin{aligned}&x-2 y+4 z=3\\&x+3 y-2 z=6\\&x-4 y+3 z=-5\end{aligned}$$

$\{(1,3,2)\}$

Algebra

Algebra 2

Chapter 4

Systems of Linear Equations

Section 3

Systems of Linear Equations in Three Variables

Polynomials

Systems of Equations and Inequalities

Introduction to Algebra

Graph Linear Functions

Write Linear Equations

Linear Equations and Functions

Matrices and Determinants

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University of North Carolina at Chapel Hill

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All right, so here our system equations X minus two y four z equals three X plus three y minus two The six finally the X minus four y plus three z. It was negative. Five. Well, you notice we even acts in every single one of these equations. What? I'm gonna do something. A software acts in this first equation to why minus poor z closely. And I'm also going to do it in the second equation. He's gonna get a six three y plus two Z. Now, you can see that these two equations are equivalent because they both equal X so you can do is you can actually set them equal to each other. You're gonna be able to solve for Z in terms of why and the other way around. So now we can see that this is gonna sim ply and is going to give us three if we ever to this three minus through I plus two wives when you mine, that's why. And if we move this to Z over equals two Z therefore, why get equal three minus two z? So now why, in terms of Z now we can do is we go back to that original problem and we said that X minus two Now have why we can substitute this vision in for why three minus two Z plus four z equals three X minus six for the 1st 4 z three, this is gonna give us X equals nine minus eight disease. So now we have X and Y in terms of Z, and we can plug these equations into the other. Any of these top three to actually solve for Z knows we have see you plug back in to solve for X and Y Let's do that here. I'm gonna use the second equation. We have X, which who knows nine minus 80 plus three times. Ally, which is three minus two z Honest to Z equals six. This up Give us more space. It was nine minus 80 plus nine on a 60 minus to see people's six. If you supply this a little bit, we have a negative 80. Negative 60. That's a good 14 minus two. Ze frank of 16 z even nine plus nine, which is a clue. Um, so we have six months eat clean, which is negative 12 and we can delete that. And this is going to give us the equals 12 divided by 16. Both of these individual by four. You divide them both my four year and get 3/4. So now we have Z equals three force we can solve for axe and why this is going to give us access equals nine on this e eight times 3/4 bu nine minus 24 out of four. 24 about afford six. So this is gonna equal three. Why it was three minus six bores because that's two times you. Just 3/4. Um, 6/4 is 1.5 feet minus 1.5 course, three haps. So now we have our order. Triple Ex Im A. Why I'm a Z equals x three. Why three have and z three courts. You could use your calculator plugged back in and make sure the solution holds. Look for these three equations

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