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Point) Solve the systemX1 +X2 X2 +x3 X3 +X4 X1 +X4-2355 -10X1X2 X3 X4+5...

Question

Point) Solve the systemX1 +X2 X2 +x3 X3 +X4 X1 +X4-2355 -10X1X2 X3 X4+5

point) Solve the system X1 +X2 X2 +x3 X3 +X4 X1 +X4 -2 3 55 -10 X1 X2 X3 X4 +5



Answers

Determine if the given point is a solution to the system. $\frac{1}{3} x=\frac{2}{5} y-\frac{4}{5} \quad(0,2)$ $\frac{3}{4} x+\frac{1}{2} y=2$

All right. So we have a system of four variables and four equations. I'm gonna take equation one, which is five w plus three x plus eight y plus the people's one. And I'm gonna pair it with the equation for which says that X plus y plus C equals zero. If I subtract those equations, I get five w It was two x plus seven y equals one. I'm also gonna take equations to and equations three and do the same brain equation too. Just tell you. Plus two X was, uh plus two Z equals three an equation. Three says four w What's what. Monet's to Z ankles. Negative three. If I had those, I get five w plus two X, which this is an X. Sorry about that. Two X plus six. Why equals zero now, if I take these two and put them together so I'm gonna bring that suspect. Wanted it in the top down five W plus two X plus seven. Why one and subtract? I'm gonna get negative. Why? He was negative born and why one? Well, what can I do with this? Because I still need to find three other variables. So Here's what we're gonna be We know that equation for says the X plus y plus Z ankles zero. So I'm gonna take equation too, which says W now if you notice it says two x five watt and two Z So I'm gonna take three of those wise and then that'll leave me with and two exes to WAAS in Twosies equals three. Well, if you know this is zero and that all goes away and we know that w then plus three y equals three. So if why is one then we get w plus three equals three and w equals zero. So I have w and ahead Walk so go toe equation gree equation three says four w plus Why minus two z equals negative three. So we have four times zero plus one minus two z equals negative three Negative to Z then equals negative four and Z People's Z equals two again w again Why I got Ziani dicks will remember One equation board says crazy for says that X plus y plus the equal zeroed It's why is one and Z is zero then That means that X has to equal. I'm sorry z is too. So then that means that X plus three equals zero on eggs equals negative three. We now have all four that we need. We know W is zero X's negative. Three. Why is one and C is to Okay, there are therefore answers to the system.

Right, We want to solve the system of the new equations given to the right by the two equations. Three X plus one, X two plus X three plus export equals zero and five. X one minus X two plus X three minus X four equals zero. To solve this, we're going to use row operations between these two equations to simplify a problem and make it more easy to identify the solutions for X +123 and four. So to start off, let's isolate X one in the top row. So we're gonna go one by three. Now we have X one plus X to over three plus X 3/3 plus X 4/3 equals zero in the exact same second row. Now let's remove X one from the second row. So we're gonna subtract five of row one from row two hands, zero operations. This turns our equations into the identical first row and now negative eight thirds X two minus two thirds, X three minus eight thirds X four equals zero. So we see that X three and X 43 variables. So if we let X four equal T, and X three equals S. We can solve row to to find X two equals negative 1/4 class minus T, and similarly, row one to find X one equals negative 1/4 S. This is because X there are only two systems of equations, or two equations for four variables to two of our variables must be free variables. Hence for varying T assets satisfy these equations written down, we have infinitely many solutions.

All right to start this process, I'm gonna take the 1st 2 equations. Okay? I'm gonna eliminate the wise in this case. And so I want to multiply this top equation then but, uh, give me five x modest. But why? Mama's tensy equals zero. And so if I had those, I get three x equals negative three and X equals negative one. Now, my third equation said three x plus y equals zero and so x is negative one that I know that why is gonna equal positive three since I now know X and why I confined Z So I'm gonna use the first equation X minus La Moniz to Z equals zero X's negative one. Why is three so negative to Z then they didn't want a negative three is negative for you. Move it over. You get four. And then dividing my negative two gives me a value of C equal to negative two. And so the points here are gonna be negative. One, three, and two and then getting to


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