Question

solve the system by elimination -2x + 2y + 3z = 0

Answer 1

UGH HELP

Answer 2

I dont see a system of equations. I only see one equation.

Answer 3

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

Answer 4

show me steps i really want to understand.

Answer 5

THANKS GUYS THANKS

Answer 6

Alright Sorry I had to look up a video :p Give me a break

Answer 7

so basically you look at it like a regular adding and subtracting equation

Answer 8

and every time you see like you do in this equation -2 and +2 they are an additive inverse which means they cancel out

Answer 9

so for you first step you look at the first column

Answer 10

you have a -2x and a positive 2x so they cancel out
so right now you have -2x left

Answer 11

for the next column you don't have any additive inverses so basically you just have to solve that column

Answer 12

which it would end up being 4y

Answer 13

so right now you have -2x+4y

Answer 14

and for the last column after adding everything it is 7z

Answer 15

so for the whole thing it would go -2x+4y+7z=2

Answer 16

Does that help at all?

Answer 17

hahahaha i was just kidding with ya, and OHHHH i solve them then add them all together? and if they have a neg i multiply the whole thing by a positive right? and if it doesnt i just solve the equation?

Answer 18

No You just solve them as they are and if it happens there is 2 of the same numbers and one is negative and the other is positive they cancel each other out

Answer 19

Like in the first part you had the negative 2 and the positive 2 those canceled out just leaving another -2

Answer 20

you are allowed to have negatives so you dont have to multiply by positives

Answer 21

but why would i have a -2 left, what about the 3z?

Answer 22

no no I am looking at this

Answer 23

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

Answer 24

on the first one

Answer 25

you take them by sections

Answer 26

You take the whole thing every equation

Answer 27

You see how they are organized so nicely into x's y's and z's

Answer 28

but on the first one i just have -2 after canceling each other out, what to i do with the 3z=o?

Answer 29

See the thing is you are not looking at it as a whole with all three equations

Answer 30

Look at the whole thing

Answer 31

I am talking about the -2x and the +2x

Answer 32

look at it vertically

Answer 33

oh i solve for x then y then z?

Answer 34

Exactly you get what each one equals and combine them all into one equation

Answer 35

so the first would be -2x because +2x and the other -2x cancel eachother out

Answer 36

-2x + 2y + 3z = 0
-2x - y + z = -3 -->(-1)
-----------------
-2x + 2y + 3z = 0
2x + y - z = 3 (result of multiplying by -1)
-----------------add
0 + 3y + 2z = 3
3y + 2z = 3

we have eliminated the x in the first two equations. Now we have to eliminate x in the last two equations.

-2x - y + z = -3
2x + 3y + 3z = 5
----------------add
0 + 2y + 4z = 2
2y + 4z = 2

Now take the equations that you eliminated the x in and eliminate another variable.

3y + 2z = 3 -->(-2)
2y + 4z = 2
---------------
-6y - 4z = -6 (result of multiplying by -2)
2y + 4z = 2
----------------add
-4y + 0 = -4
-4y = -4
y = -4/-4
y = 1

now sub 1 in for y in an equation that the x was eliminated from
3y + 2z = 3
3(1) + 2z = 3
3 + 2z = 3
2z = 3 - 3
2z = 0
z = 0/2 which = 0

now that we have y and z, sub in 1 for y and 0 for z in one of the original equations
-2x + 2y + 3z = 0
-2x + 2(1) + 3(0) = 0
-2x + 2 + 0 = 0
-2x + 2 = 0
-2x = -2
x = -2/-2
x = 1

now we can check our answers ( I recommend doing this) by subbing in known values into one of the original equations
-2x - y + z = -3
-2(1) - 1 + 0 = -3
-2 - 1 + 0 = -3
-3 + 0 = -3
-3 = -3 (correct)
If it comes out equal, then the answers are correct.

x = 1, y = 1, and z = 0

Answer 37

O_O

Answer 38

guys you both helped me so much thank you

Answer 39

o_o that paragraph is holy

Answer 40

did I explain it enough or do you have questions ?

Answer 41

yeah i think i get it now and i can do it. thank you both for your time :))

Answer 42

no problem...glad to help