Question

Solve the system by elimination. 
-2x+2y+3z=0 
-2x-y+z=-3 
2x+3y+3z=5 

Answer 1

@StudyGurl14 by any chance do you know this?

Answer 2

Ooh...yuck. I know how, but I really hate systems of equations with three variables...

Answer 3

Okay, so do you know what it means by "elimination"?

Answer 4

Im guessing I have to eliminate variables or numbers or something?

Answer 5

sorta.

Answer 6

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 7

Okay, what does it mean?

Answer 8

Okay, notice how all the equations start with either 2x or -2x?

Answer 9

It is easier to show you, rather than tell you

Answer 10

yes I see

Answer 11

You can eliminate the x variables of the equations by adding/subtracting the equations from each other.
take the first equation and the third equation
-2x+2y+3z=0
2x+3y+3z=5
______________
0 + 5y + 6 z = 5

Answer 12

okay so do that with them all? like 1,2 then 1,3 then 2,3?

Answer 13

And then, you can do the same with the first two equations
-2x-y+z=-3
multiply by -1
2x + y - z = 3
Next,
-2x+2y+3z=0
2x + y - z = 3
_______________
0 + 3y + 2z = 3

Answer 14

what do i do after that?

Answer 15

Now you have these two equations:
5y + 6z = 5
3y + 2z = 3

Answer 16

You want to eliminate one more variable so you can solve for the other variable.

Answer 17

okay..

Answer 18

3y + 2z = 3
multiply by -3
-9y - 6z = -9
See how it is changed?

Answer 19

yes but why multiply by -3? and what would multiply the 5y + 6z = 5 by would it be -5?

Answer 20

5y + 6z = 5
-9y - 6z = -9
_______________
-4y + 0 = -4
Now what?

Answer 21

I multiplied it by -3 so that the 2z would change to -6z, which, when added to the 6z from the other equation, equals zero. Make sense?

Answer 22

yes! So only one equation needs that not both?

Answer 23

right. in some cases, you might need to multiply both equations by something, but not in this case

Answer 24

So, you have
-4y = -4
What does y = ?

Answer 25

Oh okay..
oh um.. lol uhhh -4?

Answer 26

Divide both sides by -4. What is -4/-4?

Answer 27

1?

Answer 28

Correct! So...y = 1

Answer 29

thats it? or is there more?

Answer 30

There's more...lol. You still have to find the values for x and z

Answer 31

oh lol darn it.... how do i do that?

Answer 32

Okay, so we have this equation from before:
5y + 6z = 5
Now that we know y =1, how do we solve for z?

Answer 33

Im not sure..

Answer 34

maybe do the same thing or something similar?

Answer 35

Plug in 1 for y, and solve for z
5(1) + 6z = 5
5 + 6z = 5
6z = 0
z = ?

Answer 36

would it be 6 divided by 6?

Answer 37

1?

Answer 38

Nope. Hint: Any number times 0 = 0

Answer 39

oh 6 x 0? so 0?

Answer 40

Correct. So z = 0

Answer 41

So we know z = 0, and y = 1. How do we find the value of x?

Answer 42

would we use multiplication again?

Answer 43

we would plug in again.

Answer 44

using multiplication?

Answer 45

Let's use the very first original equation.
-2x+2y+3z=0

Answer 46

If z = 0, and y= 1, how would we find x? Using this equation ^

Answer 47

plug it in: -2(1)+2y+3(0)=0 ?

Answer 48

Close. We don't know the value of x yet. We know y = 1, so you would replace y with 1, not x

Answer 49

Oh i mean -2x+2y(1)+3(0)=0 haha sorry

Answer 50

Yeah I mistyped lol

Answer 51

Right!

Answer 52

Okay, so you have:
-2x+2(1)+3(0)=0
What now?

Answer 53

man.. um.. i think like this?
-2x+2(1)+3(0)=0
-2x+2+3=0
after that Im a bit stuck but i am starting to understand!

Answer 54

@StudyGurl14

Answer 55

lol 5!

Answer 56

actually..no

Answer 57

3(0) = ?

Answer 58

3? lol unsure now :P

Answer 59

Remember this rule. Whenever a number is being multiplied by 0, the result is 0. Whenever a number (except for 0) is being multiplied by 1, the answer is that number. So, in this situation, is 3 being multiplied by 1 or 0?

Answer 60

oh sorry the answer is 0 wow im dumb

Answer 61

Yep. And no you're not. It is easy to forget the simple stuff once you start dealing with super hard stuff that occupies all the space in your brian..lol

Answer 62

Okay, so back to
-2x+2(1)+3(0)=0
This would simplify to...
-2x + 2 + 0 = 0
What's the next step?

Answer 63

lol yeah my "brian" hurts right now hahaahah :P

Answer 64

lol.

Answer 65

-2x + 2?

Answer 66

Yep...I named my brain Brian. lol

Answer 67

Yep
-2x + 2 = 0
What now?

Answer 68

HAHA!! Wait how does 2x + 2 equal zero? :/

Answer 69

@StudyGurl14 ? :(

Answer 70

Because. That was the original equation...go back a few posts and look. You can't eliminate the equals sign...or the zero on the other side. Only the one zero on the left side of the = sign

Answer 71

oh okay so what would be the next step?

Answer 72

@StudyGurl14 why do you keep leaving meee we are almost done!!

Answer 73

sorry i have to check on my own quesiton

Answer 74

ok. so next step...

Answer 75

oh I thought you were mad at me lol

Answer 76

-2x + 2 = 0
- 2 -2
_______________
-2x = -2

What does x equal?

And of course I'm not mad at you.

Answer 77

4? lol thank god i need you!

Answer 78

Nope....
Divide both sides by -2
What is -2/-2?

Answer 79

oh i multiplied!
its 1 :)

Answer 80

@StudyGurl14

Answer 81

correct

Answer 82

So....
x = 1
y = 1
z = 0

Answer 83

So what do i do with those? am I done or do I need to do something else? @StudyGurl14

Answer 84

You're done

Answer 85

or should I say "I'm done" lol, jk. xD

Answer 86

No you should you helped so much thanks again Einstein!! :D

Answer 87

lol, you're welcome.

Answer 88

Hey, have you written me a fan testimonial yet? *hint hint*
lol, xD

Answer 89

No way I thought I did!

Answer 90

sometimes it glitches. maybe try again?

Answer 91

Yeah I refreshed.. so weird this will be my third time writing it!!

Answer 92

I wrote one :)

Answer 93

Thanks so much!

Answer 94

what you wrote was so nice :)

Answer 95

Of course I really value your help!!! hey for the first and third equation did you divide to get 0 + 3y + 2z = 3 @StudyGurl14

Answer 96

no I added

Answer 97

added them and the other two to get the final two equations?