Question

How do you solve this?
2x + 4y - 3z = -7

Answer 1

@Data_LG2

Answer 2

only one equation? O.o

Answer 3

Lol no, there are 3 of them

Answer 4

oh okay lol, can you post them too?

Answer 5

2x + 4y - 3z = -7
3x + y + 4z = -12
x + 3y + 4z = 4

Answer 6

alright :)

1. Let's label them first
2x + 4y - 3z = -7 --> eqn 1
3x + y + 4z = -12 --> eqn 2
x + 3y + 4z = 4 --> eqn 3

2. Choose which method you want to use, elimination or substitution? Elimination is the best & easiest way. Do you know how to apply this method?

Answer 7

I haven't done it in a while, I just did substitution in my last equation, but haven't tried elimination.

Answer 8

ok.

For solving 3 variable equations, we have to pick two equations first.
we will use the 1st and 2nd equation.

2x + 4y - 3z = -7 --> eqn 1
3x + y + 4z = -12 --> eqn 2

Let's say we want to eliminate the variable y, what will you multiply to eqn 2 so that when you add eqn 1 and eqn 2, y will get cancelled?

Answer 9

-4?

Answer 10

right!

now multiply -4 for each term in eqn 2

-4(3x + y + 4z = -12)
-4(3x) + -4(y) + -4(z) = -4(-12)

when you simplify this, what will you get?

Answer 11

-12x - 4y -4z = 48 ?

Answer 12

perfect :P

now add that to eqn 1

2x + 4y - 3z = -7 --> eqn 1
-12x - 4y -4z = 48 --> eqn (2 multiplied by -4)
-----------------

Answer 13

I am subtracting those, right?

Answer 14

since you already multiplied 2nd eqn with -4, you have to add them

I'll do the 1st term for you :)

2x + 4y - 3z = -7 --> eqn 1
-12x - 4y -4z = 48 --> eqn (2 multiplied by -4)
-----------------
-10 x

then continue it, y will get cancelled. Then add the terms with z and so on

Answer 15

-10x -7z = 41 ?

Answer 16

yes.

-10x - 7z = 41 let this be your eqn 4

Now, next step is you have to pick another pair from your equations that include eqn 3 and do this process again. Remember that we are eliminating variable y okay? :)

Answer 17

Just to be sure, now I take -10x - 7z = 41 and x + 3y + 4z = 4 and do everything we just did?

Answer 18

No, cause it doesn't have a y anymore

Answer 19

no, just leave eqn 4 (which is -10x - 7z = 41) for now. We will use it later.

Just pick any pairs: eqn 1 and eqn 3 or eqn 2 and eqn 3?
After you choose, do the process again and eliminate y

Answer 20

Okay, so if I take eqn 1 and eqn 3 how would I eliminate the y is it's a 4 and a 3?

Answer 21

Sorry if I am asking basic questions, math is not my strong suit

Answer 22

No worries! we're here for a reason :)

2x + 4y - 3z = -7 --> eqn 1
x + 3y + 4z = 4 --> eqn 3

just think about the least common factor of 4 and 3, which is 12.
If you make those y-terms 12 and -12, they will get cancelled right?

So for the 1st eqn, what will you multiply 4 to get 12?
For eqn 3, what will you multiply 3, to get -12?

Answer 23

1st eqn by 3 and 3rd eqn by -4

Answer 24

right :)

So multiply eqn 1 by 3 and multiply eqn 3 by -4 ... then add these equations together

Answer 25

I got 3x - 7z = -3 ?

Answer 26

Oh i forgot to multiply it to everything in the equation!

Answer 27

let me see :)

3(2x + 4y - 3z = -7) --> eqn 1 x3
6x + 12y -9z = -21

-4(x + 3y + 4z = 4 ) --> eqn 3x -4
-4x - 12y -16z = -16

6x + 12y -9z = -21
-4x - 12y -16z = -16
------------------
2x - 25z = -37

hmm I get a different one.
:)

It's okay, so now let this be eqn 5

Now let's combine eqn 4 by eqn 5:
-10x - 7z = 41 --> eqn 4
2x - 25z = -37 --> eqn 5

You can use either substitution or elimination to combine these two and solve for the variables x and z. Can you manage this part?

Answer 28

Okay, I was going to do substitution but then I got confused, where I would put 41 and -37?

Answer 29

I'm not sure what you mean... can you show me your steps so that I can check? :)

Answer 30

Well I'm not really sure what to do, as this lesson is about learning sub and elimination, but I think I would start by putting something like -10x -7 ( ? ) = ? do you get what i'm saying?

Answer 31

yes, that's right.

-10x - 7( ? ) = 41

You have to rearrange eqn in terms of z so that you can substitute it into the eqn 4.
2x - 25z = -37 this should be z=

Answer 32

what do you mean? z = ?

Answer 33

for example: you have equation
2x - 3z =4
arrange this in terms of z
so it will be like