Question

If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and second equations, then the second and third equations.

x + y – 3z = –8
2x + 2y + z = 12
3x + y – z = –2

Answer 1

Okay, let's walk through it. What would you do to eliminate z in the first and second equations?

Answer 2

divide -8 by -3z for the first one. @whpalmer4 please correct me if I'm worng.

Answer 3

x + y = –8
3x + y = –2

x + y = –8
5x + 3y = 14

7x + 7y = 28
3x + y = –2

7x + 7y = 28
5x + 3y = 10

Answer 4

To eliminate z from
x+y-3z = -8
2x+2y+z=12
we multiply the second equation by 3, so that we have
x+y-3z=-8
6x+6y+3z=36

and if we add the two equations together, the z terms cancel out, leaving us with
7x +7y = 28

Answer 5

In the second and third equations, we don't have to do any manipulation, just add them:
2x+2y+z=12
3x+y-z=-2
5x+3y=10

So @lornbeach nails it!

Answer 6

or no, she was just posting answer choices...
I was wondering about some of those steps :-)

Answer 7

hahahah (:

Answer 8

I was hoping!

Answer 9

Do you see how I do the elimination?

Answer 10

yes

Answer 11

The easiest eliminations are like the 2nd and 3rd equations, where you conveniently already have the coefficient of 1 term being equal but opposite in sign. Sometimes you'll have a coefficient which is a multiple of the coefficient in the other equation, then you multiply and combine. And sometimes you have to multiply one by the other and the other by the first, such as
2x -3y = 6 (multiply by 2)
3x +2y = 0 (multiply by 3)

Answer 12

i understand that

Answer 13

would the answer be
7x + 7y = 28
3x + y = –2
or
7x + 7y = 28
5x + 3y = 10

Answer 14

Which answer choice contains the equations I found by elimination?

Answer 15

they both contain it but there is another that needs to be found

Answer 16

No, I came up with 2 equations...separate posts...

Answer 17

hint: the one where I said you nailed it has the second one :-)

Answer 18

oh awkward my bad, so the first one

Answer 19

why do you say the first one? Look at the equation I came up with in that post...

Answer 20

like the first of the two i put up recently

Answer 21

im totally not looking at the right one hahahah sorrry

Answer 22

Really? 3x+y=-2 looks like 5x+3y=10?

Here's the post I was referring to:
"In the second and third equations, we don't have to do any manipulation, just add them:
2x+2y+z=12
3x+y-z=-2
5x+3y=10

So @lornbeach nails it!"

Answer 23

i was looking at the wrong post hahah my bad!

Answer 24

Attention to detail is important — lots of mistakes are just inattention after doing substantially the right thing. Nothing worse than figuring out the right answer but getting it marked wrong because you copied the wrong thing, or something silly like that!