Question

solve the system using any method.
x+3y+z=2
4x+y+2z=-4
5x+2y+3z=-2

Answer 1

Do you have a favorite method you like to use on these?

Answer 2

no but I tried the addition method but it dindt work out

Answer 3

Technology not allowed, right?

Answer 4

@teyo212
Let's go with addition/subtraction.
Let's eliminate z.

Or, we could go for eliminating the variable you used.
Just let me know. @teyo212

Answer 5

that's fine

Answer 6

x = -4
y = 0
z = 6

Answer 7

1) x+3y+z=2
2) 4x+y+2z=-4
3) 5x+2y+3z=-2

I'm numbering these equations as 1, 2, and 3.
The object here is to eliminate variable z in all 3 equations.
First, we'll eliminate variable z in equations #1 and #2.

I'll need you to help because if I just post a solution, I'll be banned from the site.
The idea of this site is to have an exchange between the Asker and the Answerer.
So, help me out, please. c:

Answer 8

@kulprit
OpenStudy values the Learning process - not the ‘Give you an answer’ process
http://openstudy.com/code-of-conduct

Answer 9

eliminating z from 1) and 2) you arrive at 2x-5y=-8
eliminating z from 1) and 3) you get 2x-7y=-8 ----- (4)
clearly y=0 and from (4) you get x=-4
so from (1); z = 2-(-4) = 6
[x y z] = [-4 0 6]

Answer 10

@teyo212 Would you like to continue?

Answer 11

yes please

Answer 12

What do you get when you multiply the first equation by -2?
------

1) x+3y+z=2
2) 4x+y+2z=-4
3) 5x+2y+3z=-2

Answer 13

-2x-6y-2z=-4

Answer 14

Yes.
To eliminate z in equations 1 and 2 add what you posted:
-2x -6y -2z=-4
4x+ y+ 2z=-4
=============
Post the results of the addition, please. Thanks.

Answer 15

You are adding your workk to equation 2 to eliminate z. That was the purpose of multiplying the first equation by -2.

Answer 16

2x-5y=-8

Answer 17

Correct.

We need to keep track of that
2x-5y=-8 ***

Now..

Answer 18

Next up is to eliminate z in equations 1 and 3. To do this, we will multiply equation 1 by -3 and then add that result to equation 3.

Your task is to multiply

x+3y+z=2 by -3 and to post the result here.

Answer 19

2x-7y=-4

Answer 20

-3x - 9y - 3z = -6
5x + 2y + 3z = -2
=============
2x -7y = -8

Answer 21

I think you may have forgotten to multiply the 2 of equation 1 by -3.

Answer 22

Do you agree with this result:
2x -7y = -8 ? ****

Answer 23

yes

Answer 24

We have now "reduced" the 3 by 3 system to a 2 by 2 system:

4) 2x-5y=-8 ***
5) 2x -7y = -8 ? ****

To eliminate x, multiply equation 4 by -1 and add to equation 5.

Please post the result.

Answer 25

y = ?

Answer 26

1

Answer 27

4) 2x-5y=-8 --by -1 --> -2x + 5y = 8
5) 2x -7y = -8
----------------
-2y = 0
y = 0 ##

Answer 28

Substitute 0 in for y in this equation and solve for x.
4) 2x-5y=-8 ***
@teyo212

Answer 29

that 2x-7y=-8 suppose to be a -4

Answer 30

I don't follow what you are saying.

Answer 31

never mind

Answer 32

You wrote it earlier in the post: 2x-5y=-8

Answer 33

Will you do this: Substitute 0 in for y in this equation and solve for x.
4) 2x-5y=-8 ***

Answer 34

-4

Answer 35

In equation 1, x+3y+z=2
substitute 0 for y and -4 for x and solve for z.
That will be the end of the problem because we will have values for x, y, and z.

Answer 36

6

Answer 37

So the solution is (-4, 0 , 6)

Answer 38

ok thank you for your help

Answer 39

Glad to help.