Question

what is the solution.. medal.

3x + 2y + z = 7
5x + 5y + 4z = 3
3x + 2y + 3z = 1

Answer 1

Do you know how to solve 3 equations at a time? You must be in Algebra 2?

Answer 2

i am in alg. 2 but idk how to do it :/

Answer 3

Give me a couple of minutes to work it out then I will be able to take you step by step. Is that ok with You?

Answer 4

yeah :) thanks!

Answer 5

Multiply the first equation by -4 and post the result.

Answer 6

multiply where though?

Answer 7

He means the whole equation. Multiply everything in the first eqaution by a -4.

Answer 8

The first equation which is 3x+2y+z=7

Answer 9

-12x + -8y + (what you do with "z") = ?

Answer 10

\[-4(3x+2x+z=7)\]=-12x-8x-4x=-28

Answer 11

typo: -12x-8y-4z=-28

Answer 12

Now write the second equation underneath that and add the two equations

Answer 13

Add those

Answer 14

-7x + -3y + 0z = 31

Answer 15

-28+3 is NOT 31

Answer 16

-25 didnt see negative. im sorry.

Answer 17

What is 0 times z?

Answer 18

anything times 0 is 0... so 0?

Answer 19

So now we have the equation: -7x-3y=- 25

Answer 20

Do you notice that we have eliminated the z ?

Answer 21

yeah

Answer 22

We have to do that again and we have to use the third equation which hasn't yet been a part of the solution. So this time multiply the first equation by -3 and post the result.

Answer 23

the original first equation?

Answer 24

yes

Answer 25

-9x + -6y + (again, forgot what you do with z) = -21

Answer 26

z means 1z.
Everyone agrees that if the coefficient is a 1 we won't bother to write it and everyone will just know that it is there.

Answer 27

-3(3x+2y+1z=7)
-9x-6y-3z=-21

Answer 28

Now add the third equation to that result.

Answer 29

-6x + -4y + 0z = -20

Answer 30

yes. Do you notice that the z has been eliminated again since 0z = 0 ?

Answer 31

yeah

Answer 32

So now we have two equations with only x and y and they are:
-7x - 3y = -25 and
-6x - 4y = -20

Answer 33

Can you solve that system?

Answer 34

yeah... got it from here! thanks :)

Answer 35

yw