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VD~ Av < AEy ECalibri LightSolve the linear System algebraically. (10 polnt: eacb) -x+ytz=-2 5x + 3y + 32 = 71 4 - 2y - 32 = 16r +Y =323-19 F + 5]= 5 3t +) +63 =...

Question

VD~ Av < AEy ECalibri LightSolve the linear System algebraically. (10 polnt: eacb) -x+ytz=-2 5x + 3y + 32 = 71 4 - 2y - 32 = 16r +Y =323-19 F + 5]= 5 3t +) +63 = 17

VD~ Av < A Ey E Calibri Light Solve the linear System algebraically. (10 polnt: eacb) -x+ytz=-2 5x + 3y + 32 = 71 4 - 2y - 32 = 1 6r +Y =323-19 F + 5]= 5 3t +) +63 = 17



Answers

Solve each system of linear equations by substitution. $$\begin{array}{rr} 5 r-3 s= & 15 \\ -10 r+6 s= & -30 \end{array}$$

We have the system of equations. 7.2 x minus 4.1 Y equals 7.0 and negative 3.5 X plus 16.5 Y equals 2.4. We want to solve this with the substitution method so I'm going to rearrange the first equation to be 7.2 X minus 7.0 equals 4.1 Y. And then divide everything by 4.1 and you'll get y equals 72/41 X minus 70/41. Now take this and substituted in for wine and second equation. So we get negative 3.5 X plus 16.5 times 72/41 X minus 70/41 equals 2.4. Do some simplifying here, we get negative 3.5 X. When we distribute the 16.5 as a fraction, that's 11 88/41 X minus 11 55/41. Now we'll divide um now we can combine our exes and we'll get negative 2089 over 82 X. And we'll add the 11 55/41 to the 2.4 to get 60 to 67/2 oh five. Now divide both sides by negative 20 89/82 you'll get X equals 1.2. Take this and substituted into one of the two equations. It doesn't matter which one I'm going to plug it into. Are simplified version 72/41 with an X value of 1.2 minus 70/41 gives us a Y value of 0.4, so X is 1.2 and Y 0.4 busy.

Okay, so we're asked to solve falling. So let's start by. Let's see, multiplying our second question. Vice Negative. Five. So are yet negative. Five X plus 15 white minus five C is equal to 50. And now I'm going to use our first equation. We have five x plus seven white. You go to Tony and I'll combined Easter. So we get 15.7 is 22 y minus five. Z is equal to 70 Now. I'll use our this equation here in this to combine it. So we'll multiply this equation here by negative 11 to get rid of our wife. So we get negative. 22. Why? Minus 55 c is equal to negative. 11 times 50 is negative. 5 50 Okay, No, something them yet or wise counsel. You have negative. 60 z is equal to negative from zero well 70 which is negative for 80. Inviting by 16. Yet that d physical to H. No, it's all for, um it seems we have ZZ go to eight so we can use 22 y minus five z, which is eight. Is he could assembly to solve. For why so that's four times h is negative. 40. Adding 40 Get seven depots. 40 which is one ton. Is it good to 22? Why? Dividing by 20? To get that, why is equal to five? And now we just need to solve for X. You know that five X plus seven wine, which is five u 20. So that's 35. You get 20 Sobchak, 35 signs. We get negative. 15 is equal to five x Between that X is equal to negative three. So we get that X isn't gonna three. Why is five NZ is it?

Arrest, assault, the system using elimination. And when you can notices, it's gonna be easiest to eliminate. Why? Because always to do is multiplied to stop equation like to to have 10 y in 10 1 So if we do that Oh, is there? Well, we have to. All we have to do is add these two equations together it So we have two times two acts. That's for acts. Plus, the reacts gives us seven x two times five. Why, it's 10. Why? Plus negative 10. Why that zero? Why? And then we have 14 plus five. Could be 19 until X is gonna equal 19. About by seven. Once we know that we can say OK, well, two times 19 of seven plus why seven? Now you use okay, 30 by seven. Plus five. What I people seven. I've lies going to equal 79 38 around about seven. You know, seven of the same 49 7 So five. Why so equal 11 Divided by seven. Oh, well, we have to do is divide both sides. The equation by five. Excuse us. Why equals 11 about a great cause? We multiply seven. I'm sorry if we're dividing by five. All right, so now we have our solution. X equals 19/7. Why? It was 11 over.

We're going to solve the system using the elimination method. So that means that we're going to try to get the coefficients on one of the variables to be opposites so that we can add the equations and that variable will cancel. So I'm going to work on getting the S coefficients to be opposites. So I'm going to multiply the first equation by five and the second equation by three. So the first equation becomes 25. Ar minus 15 s equals 120 and the second equation becomes nine r plus 15 s equals, Let's see what 28 times three is 84. Okay, so when we add the equations, the S terms were going to cancel, and we have 34 are equals 204. Now, we're gonna divide both sides by 34 and we get our equal six. Now, to find the value of s, let's go ahead and substitute that number into one of our equations. We can use the first equation. Five R minus three s equals 24. So five times six minus three s equals 24. We have 30 minus three s equals 24. Subtract 30 from both sides and negative three s equals negative six and divide by negative three and we get asked equals two. So our solution as an ordered pair in the order are common s would be six comet toot.


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