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Solve each system of equations.

$$\begin{aligned}3 x-4 y+z &=19 \\2 x+4 y+z &=0 \\x-2 y+5 z &=17\end{aligned}$$

$\{(3,-2,2)\}$

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

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All right. So you're giving in Equation three x four. Why c equals 19 two x those four y z zero and X minus two y plus five p equals writing. All right, Sorry. 17. So I see a to To To out here for why here in a four y here. Something we can use elimination and eliminate. Why? So if we add these 1st 2 operations together, five acts zero Why A to Z equals night kids. And now, if you multiply the start equation by two, that's gonna leave us with. So it's gonna be, um we're gonna have to subtract. So it's gonna be three x minus three x zero x negative for Why mine those. I were most finance by two because we want the four wide four wives to cancel. So it's gonna be three x minus two x Just gonna be X negative. Four y minus Negative. Two y zero Z minus 10 Z B minus nine. Z equals 19 minus 34. Which is gonna be negative. 15. All right, so now we can solve for X and Z, right? We have X equals knives e plus 15 so we can put bread and up here to get five, five times 90 plus 15 lost. Uzi Legal 19. This is gonna give us 45 Z plus 15 times five 45 Z plus 75 45 p plus 75 close to Z. So it's gonna be 40. 70 equals 1975. It's gonna be negative. 56. You see, here we get a really weird number which tells us that we probably made him steak earlier on, and it turns out we did. Um, this nine z, it's gonna be a minus here now, plus right. So that's gonna change things. We have 90 minus 15 Now, this is gonna give us 45 acts minus 75 plus two to, um, sorry. This should be easy crossed. Uzi People's 19 on this is gonna give us 75 plus 19 94 divided by 47. This is gonna give us C equals two, which makes a lot more sense once we have the equals two. We complain that in and we get X equals three. And now we just plugged back in and salt for a while to use the second equation. Since I like that zero there. Two x six plus four. Why? Plus Z plus two equals zero on before you get four y equals negativity or why equals negative to Now we have our order. Triple X Y Z equals three comma. Negative. Two comma. Two. You could double check. This solution works. Remember? Like we ran into a little mistake and we got number. That really didn't make sense. Um, it's not likely they would give us that. We're stranger. A fraction as an answer. So you go back, retrace your steps. Syrian steak is, um and then you end up at the sluice.

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