Question

Can someone please help me with this Algebraic question? I need to be walked through it, because I have no clue how to solve for it. This is for Algebra 2.
1. Solve the system by Elimination.
x + 5y - 4z = -10
2x - y + 5z = -9
2x - 10y - 5z = 0

Thank you in advance and whomever is able to help will receive medal :)

Answer 1

yes

Answer 2

Okay, so what do we do? @civicsiscool44

Answer 3

what are your answer choices if any

Answer 4

Okay! Hold on.

Answer 5

A. (5, -1, 0)
B. (-5, 1, 0)
C. (-5, -1, 0)
D. (-5, -1, -2)

Answer 6

@civicsiscool44

Answer 7

I'M 78% sure its d

Answer 8

don't forget to fan me

Answer 9

Okay. Do you think you could explain a little to me how to do it? @civicsiscool44

Answer 10

well i have done this before and i know the answer is right

Answer 11

It wasn't that I didn't trust your judgement, just that I really need help with knowing how to do this stuff lol xD but yeh, thank you. I'll give you your medal for trying. :) thank you! @civicsiscool44

Answer 12

@ospreytriple , do you think you could help explain the problem to me? Like, how to solve it?

Answer 13

not really i'm really good at explaining math problems

Answer 14

The method of elimination involves adding or subtracting entire equations in order to eliminate one of the variables. If I may refer to the equations in your problem as equations 1, 2, and 3, you can add equations 2 & 3 together to eliminate the variable z.

Answer 15

Okay. Okay, gotcha @ospreytriple

Answer 16

2x - y + 5z = -9
2x - 10y - 5z = 0
------------------
4x - 11y = -9

Get the idea?

Answer 17

Yeh, I'm starting to a little. Thank you :) @ospreytriple

Answer 18

Next, you'll have to add or subtract a different combination of the three equations to eliminate z from. Can you do that?

Answer 19

How about multiplying equation 1 by 5 and equation 2 by 4 and then adding the two results together?

Answer 20

I'm trying to think of how I would do that, but I'm not sure. I don't know where to start. @ospreytriple

Answer 21

OK. Let's work with equations 1 and 2 and try to eliminate the z term.

Answer 22

Notice that in equation 1, the coefficient of z is 4 and in equation 2, the coefficient of z is 5. We can't eliminate z unless the coefficient is the same in both equations.

Answer 23

Okay. So do we move on to the ys and xs?

Answer 24

Not yet. We have to eliminate z again from a different pair of equations. As I'm trying to explain, we can attempt to eliminate z by combining multiples of equations 1 and 2. Understand?

Answer 25

Ohh yes. Equations 1 and 2, both share 5z.

Answer 26

No. Equation 1 has 4z and equation 2 has 5 z. We have to make the coefficients the same.

Answer 27

Not 1 and 2, but 2 and 3, I mean.

Answer 28

Ohh, okay.

Answer 29

The LCM of 4 and 5 is 20, so multiply equation 1 by 5 to make its z coefficient 20. Then multiply equation 2 by 5 to make its z coefficient 20. Can you do that?

Answer 30

Sirry. Multiply equation 2 by 4.

Answer 31

What do you get if you multiply equation 1 by 5?

Answer 32

20?

Answer 33

No. Multiply the whole equation...all the terms.
x(5) + 5y(5) - 4z(5) = -10(5)
What does that give you?

Answer 34

1 + 25 - 20 = -50? But that wouldn't work, because of the different variables..

Answer 35

5* + 25 - 20 = -50

Answer 36

No. You can't drop the variables. For example, what do you get when you multiply\[3x \times 4 = ?\]

Answer 37

12x ?

Answer 38

Very good. Now try multiplying the whole equation 1 by 5. You got the coefficients correct a moment ago, but you can't drop the variables.

Answer 39

5x + 25y - 20z = -50

Answer 40

Perfect. Maybe call this equation 4. Now, in exactly the same way, multiply equation 3 by 4. What do you get?

Answer 41

Sorry. Oops. Multiply equation 2 by 4. My bad.

Answer 42

Oh. Okay lol you're good, thank you for being patient with me. 8x - 4y + 20z?

Answer 43

Excellent. But don't forget the -36 on the right hand side. Call this equation 5. Carefully examine equations 4 & 5. If you add them together, you will eliminate the z term again. Can you do that?

Answer 44

Oh, we include the = 9 part? Gotcha. Okay, hold on.

Answer 45

13x + 29y + 40z? Or do we take both the 20s and cross them out?

Answer 46

Add these two:
5x + 25y - 20z = -50
8x - 4y + 20z = -36
--------------------

Answer 47

13x - 29y + 40z = 86

Answer 48

Not quite. What do you get when you add 25 and -4 ?

Answer 49

Opps, sorry! 21y

Answer 50

Good. Now add 20z and -20z. What do you get?

Answer 51

That's zero

Answer 52

Yayyy! ELIMINATION. Now, on the right hand side, add -50 and -36. What do you get?

Answer 53

Ahaha ^.^ wait, so you add -36 to each side?

Answer 54

so,
-50 -36
-36 -36 ?

Answer 55

NO! Add the right hand sides together just like all the other terms. What do you get when you add -50 and -36?

Answer 56

86

Answer 57

How about -86?

Answer 58

Oh okay, yes

Answer 59

Alright. To sum up, the addition of equations 4 & 5 looks like this:
5x + 25y - 20z = -50
8x - 4y + 20z = -36
--------------------
13x + 21y = -86

You OK with this? We're getting closer to the answer.

Answer 60

Yes. Were good :) sorry for my slowness lol.

Answer 61

No problem. Stay with me for another few minutes and we'll be done. What we've done so far:

Added equations 2 & 3 together to give 4x - 11y = -9
Added 5 times equation 1 and 4 times equation 2 to give 13x + 21y = -86

Now we have completely eliminated z from the problem. We're down to only two equations with only x & y in them. Let's now try to eliminate y, OK?

Answer 62

Okay

Answer 63

Notice that the first equation above has -11y and the second equation above has +21y. In order to eliminate y we have to make the coefficients the same. The LCM of 11 and 21 is 231. So you'll have to multiply the first equation by 21 and the second equation by 11. Can you do that?

Answer 64

Yeh, hold on. Let me try and work it out on paper :)

Answer 65

Take your time...

Answer 66

84x -231y = -189

143x + 231y = -946

Answer 67

Excellent. Now add these two equations together to eliminate y. What do you get?

Answer 68

Okay. 84x -231y = -189
143x + 231y = -946
227x + 0 = -757

Answer 69

Check the right hand side. Add -189 and -946.

Answer 70

-179572

Answer 71

No. Are you using a calculator?

Answer 72

Yes

Answer 73

OK try again.
-189 + -946 = ?

Answer 74

1135?

Answer 75

How about -1135?

Answer 76

That's what I got doing it on paper, cause my calculator kept giving me different answers

Answer 77

Yes. Sorry, I keep thinking that two negatives added together make a positive..

Answer 78

Good. So now you have 227x = -1135. y and z have been eliminated. Can you solve for x?

Answer 79

227x -1135
227x 227x

227x crosses our and becomes zero.
x = 1130?

Answer 80

No, to solve\[227x = -1135\]you would divide both sides by 227, i.e.\[\frac{ 227x }{ 227 } = \frac{ -1135 }{ 227 }\]\[x = ?\]

Answer 81

That's what I meant.

Answer 82

What do you get when you divide -1135 by 227 ?

Answer 83

Sorry, it's my stupid calculator. I think it's broken. Hold on :) -5?

Answer 84

That's right, x = -5. Now go back and find one of your equations with just x and y in it. Put -5 in for x and solve for y. Pick the simplest equation you can find.

Answer 85

Just a random equation, and do this? 4x(-5) - 11y = -9

Answer 86

That's right, but there won't be any x. You'll replace x with -5.

Answer 87

4(-5) - 11y = -9
Solve for y.

Answer 88

Ohhh, okay! Gotcha. Thanks :)

Answer 89

What do you get for y?

Answer 90

-20 - 11y = -9
11y 11y
-20 - 0 = ?

Answer 91

Do I multiply or divide?

Answer 92

-20 - 11y = -9
First, add 20 to both sides. What do you get?

Answer 93

-20 - 11y = -9
-20 -20
20 crosses out and becomes 0. Then, 11y + -20 = -9

Answer 94

No. You added 20 twice to the left hand side. Just add 20 to left hand side and add 20 to the right had side,
-20 - 11y + 20 = -9 + 20
What do you end up with?

Answer 95

31 + 11

Answer 96

No. Look at just the left hand side. You have a -20 and a +20. When you add them, what do you get?

Answer 97

0