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Solve each system of equations.
$$\begin{aligned}2 x+3 y+z &=13 \\-3 x+2 y+z &=-4 \\4 x-4 y+z &=5\end{aligned}$$
$\{(3,2,1)\}$
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
University of Texas at Austin
Oregon State University
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All right. So here we have our system of equations, and you can notice that there's a Z in every single one of these equations. So I'm you gonna use actually strategy called elimination where you could take, um, these 1st 2 equations and subtracted. So you literally you do two x minus Negative three x three y minus two y and Z minus e. And that eliminates disease. All right, we're gonna get, um, you get five X. That's why equal 70 now you can do is you can take the first equation and subtract the third equation. So you're gonna get negative two x seven. Why equals thief value of a system to equations into a notes. You can solve facts. Why? Let's do that. Using substitution, we have the why equal 17 minus five X mounts played God in no, you to acts triple seven times 17 minus five X equals eat. Um, well, negative. Two acts close. 1 90 minus 35 acts People's eat Believe this lining us more space Now we're gonna have a negative 37 acts equals negative 1 11 So X is gonna equal three. What we've actually was three weeks like that into this equation right here. Um, this is gonna get us, uh, 15 plus y equals 17. And therefore wise gonna equal to Allegri Vex and why we can plug it into this first equation or any of them to solve for Z two times X at six plus three times Live also six because the 13 therefore Z equals one. So now we have our order Triple X comma Y Z. We're just gonna equal 321 There's the after you've got the check by plugging these numbers into these three.
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