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Solve each system of equations.
$$\begin{aligned}x-3 y+2 z &=-11 \\2 x-4 y+3 z &=-15 \\3 x-5 y-4 z &=5\end{aligned}$$
$\{(1,2,-3)\}$
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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All right. So you were giving our system of equations. What Salter acts here actually was negative. 11 plus three y minus two Z oak solve for X. Ah, here is gonna give us two acts equals for why honest three z by this 50 so X is gonna equal to y. Write us 3/2 Z minus 15/2. Now, we have these two equations weaken set of equal to each other. Um, and this is gonna give us negative. 11 plus three y minus two z equals, Do I Biased rehabs comes E minus 15/2. Now, we can simplify this a little bit. It's too wise gonna turn into just why Over here. Um, if you take native three halves and then add to you're gonna get just 1/2 z over here and then if you take negative 11 plus 15 about about two, you're gonna get negative three. But I have over here gonna leave you with 1/2 z equals negative. 3.5, plus why or why equals 1/2 of doing term Lewsey z equals Why minus seven. That's now even equation for Z in terms of why at X in terms of y and Z. Let's play this equation in for Z here. Um and then we have everything in terms of why and then we can solve for why. All right, so X equals negative. 11 plus three y minus two times two Y minus seven. This is gonna give us X equals negative 11 plus three. Why minus for why? Plus 14. Which is gonna give us three minus. Why it's now. We have x NZ in terms of why someone used this last equation. Three X minus five y minus four z to actually solve for Why so we have three times three minus Why minus why minus four comes to why minus seven peoples if nine minus three Why honest five y minus ey close 28 People's five Combine like terms. Here we have a negative three. The native five. That's negative. Eight minus C is negative. 16 even nine plus 28 uh, maybe 37. And you do five minus seventh Gonna be left with negative 32 and therefore why is gonna equal to we've solved for why we complete that back in two softer accents. E X equals three months. Why did he call one? Z equals two. Wainaina. Seven equal. Negative three. Now we have our order, Triple X. I'm a wife. I'm Aziz. Equal. One common too common. Negative. Three. You conclude these back in to make sure they work.
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