Problem

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

03:42

Problem 17 Medium Difficulty

Solve each system of equations.

$$\begin{aligned}2 x-y+z &=10 \\3 x-2 y-2 z &=7 \\x-3 y-2 z &=10\end{aligned}$$

Answer

$\{(1,-5,3)\}$

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Algebra

Algebra 2

Algebra for College Students

Chapter 4

Systems of Linear Equations

Section 3

Systems of Linear Equations in Three Variables

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Video Transcript

All right. So I'm going to use elimination to solve a system of equations you can notice that shared negative to Z in both of these, the second and third equation here. So what I'm gonna do is I'm actually subtract thes two equations from each other. You can literally just draw a line right here, put a little subtraction sign and then subtract down the columns. So three x minus x gonna be two X. You have to. Why, minus negative? Three. Why is gonna be plus why this is gonna be plus zero z equals negative three. And so we actually have to do this for another to set another two equations in the system so that we can have another equation for accent. Why? So what we have to do is with the multiply this top equation by two. This is gonna give us four X minus two y plus two z people's 20. And you allowed to do that? You're allowed the most by every single term in equation by the same number, because there will still be the same equation, right? You can always just fact out of two and divide through. Um, so now What I'm gonna do is I'm a stack of this equation on top of this second equation. This time we're gonna have to add them together. So this is gonna give us four X plus three x seven axe Negative two y plus negative two y's negative for why? And then we have two Z plus negative to Z that zero z this gonna equal 27. Now we have the system equations that we can solve. Why equals negative Freon minus two acts, two acts. And I would complete this in for, um Why? Right here. Things is going to give us seven X minus four kinds. Negative. Three minus two X equals 27. This is gonna give us over here started. Keep it consistent. Seven acts plus 12 plus eight X equals 27. Remove this 2012 over. Sorry, we're gonna have 15 on this side 27 months. 12 15. And then if we added 78 acts were actually get 15 acts, therefore, X equals one. Once we have that X equals one, we can put that into this first equation to time acts. That's gonna be two plus y equals negative three. So Why is gonna equal? Um, negative five. Sorry. This work, it's kind of messy, but once we have y equals negative five and X equals one, we can plug that in any of these equations to solve for Z. So let's use the 3rd 1 x one minus three times negative five minus two Z equals can. This is gonna give us one plus 15 at 16. Minus two. Z equals 10. Um, this is going to this negative to Z equals negative six. Therefore, Z I was gonna equal through. Now we have our order. Triple X y Z equals X. Which one wise negative five and his eagles three, you just got.

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