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Solve each system of equations.
$$\begin{aligned}2 x-3 y+z &=-9 \\-2 x+y-3 z &=7 \\x-y+2 z &=-5\end{aligned}$$
$\{(-1,2,-1)\}$
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
Johns Hopkins University
Michigan State University
University of Michigan - Ann Arbor
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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'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'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'll be left with negative Y minus three Z equals one. If you use this Y equals one minus Z, you're gonna get negative One. Plus, is he minus three Z equals one, which means you're gonna get negative two d equals two and therefore because he equals negative one. Well, it'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's negative. Eight plus and plus the negative one. That's 99 the other two equations will hold as well. So you have your answer.
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