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Solve each system of equations.

$$\begin{array}{l}x+y+z=2 \\x+2 y-z=6 \\2 x+y-z=5\end{array}$$

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

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 Washington

Oregon State University

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right. So this problem were given this system of equations, it's these 1st 3 equations right here. Don't not this two x or three. Like was he X plus y plus Z equals two X plus two y minus Z equals +62 x plus y minus Z equals five. So my first steps actually gonna be to solve for Z in this equation? I used this first equation are here. I saw frizzy tu minus y minus X. And when I did, was I plug this to minus y minus axe into these 2nd 2 equations right here. So I went to, um Sorry X plus two y minus to plus y plus X equals two x plus three Y uh equals eight when you moved that to over and then you have a two x plus y. My zeke was five. Um, when you played that Z and you end up getting three x plus two, I equals seven. Now we have these two equations with two unknowns, will consult tracks and why we can say that to acts equals B minus three. Why so X is gonna equal four finest three halves? Why get rid of this And if we put that into our second equation with three times acts, which is four minus three house Why plus two I equals seven. If we multiplies out, we're gonna 12 minus 9/2 y plus for over two. Why close seven. And once we saw this, we're going to have negative five over to fly. It was negative. Five. If you divide negative five, founded by negative five over to get why equals two. But this wife was too back in ah to this equation are here. You're going to get acts equals one. So now it's pointed these in to our two equations up here to make sure our ex wives make sense. We have two times acts that's too plus three times y six equals eight. Then we have three times acts. It's gonna three plus two times why that's four equal seven. So that makes sense and delete all this work. And we have that life was to annex equals walk. Now we can just use this first equation to solve for Z, we have acts of just two beside one. That's why with just two plus Z equals two, this is gonna give us C equals negative one. So now we have our ordered pair acts. Why? Z equals one to negative one person. Preface, ease! And we have our answer.

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