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Solve each system of equations.

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

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

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

University of California, Berkeley

University of North Carolina at Chapel Hill

Michigan State University

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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'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'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'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's negative. 15 subtracted nine. And that'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

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