can someone tell me whats the right mathematical approach to

>>358596
Set up a 3x3 matrix and a vector and solve that way

That's the correct approach.

I prefer reducing the variables, so:
P = 6 - J
gives:
3S + 3(6 - J) = 12 → 3S + 18 - 3J = 12
so you can do
6S - 6J = 2(12 - 18)
6S + 6J = 12 +
--------------------------------
12S + 0 = 2( -6 ) + 12

or 12S = 0 → S = 0

this also means that P gets 4 pound and J gets 2 pounds

2J + 2P = 2(2) + 2(4) = 4 + 8 = 12

File: wat.jpg (31KB, 500x498px) Image search: [Google]

31KB, 500x498px

>>358605
lets pretend im an idiot. can you explain that to me?
am i getting closer?

6J + 6P + 0S = 36
0J + 6P + 6S = 24
6J + 0P + 6S = 12

File: mind-blown.gif (4MB, 315x210px) Image search: [Google]

4MB, 315x210px

>>358609
my almonds are in space
thanks

>>358611

Yes. And now it's a normal linear equation system, 3 variables, 3 equations->1 solution if any, apply the normal Gaussian algorithm.

>>358609
i still dont get it. how do you get to
>12S + 0 = 2( -6 ) + 12
?

>>358617
how do i apply the prussian sambarhythm

>>358617
can you even apply gauss if the variables are multiplied by 0?

>>358622

First write it in shortened form, eg
" 1J + 1P + 0S = 6" becomes 1 1 0 | 6
Now write the three equations like this:

1 1 0 | 6
0 1 1 | 4
1 0 1 | 2

One possible way would be subtract equation 1 from eqation 3

1 1 0 | 6
0 1 1 | 4
0 -1 1 | -4

Now you can add e2 to e3 so only one variable remains

--> 0 0 2 | 0 --> S = 0

Put that in e2: --> P = 4
Put that in e1: --> J + 4 = 6 --> J = 2

>>358622
He added the two equations above the dotted line together. The 6S + 6S = 12S, the J's cancel out, then the right side of the equations get mashed together. 12 - 18 = -6.

>>358631

Of course you can. More than one zeros but less than all but one just increase number of steps needed. If all variables are multiplied by zero then this equation simply does not exist and if all but one are zero you already have a variable defined, meaningg one variable and one equation fall away.

File: transcended.jpg (9KB, 249x202px) Image search: [Google]

9KB, 249x202px

>>358633

i) 6J + 6P = 36
ii) 6P+ 6S = 24
iii) 6J + 6S = 12

i-ii) 6J - 6S = -12
ii-iii) -6J + 6P = 12

iii-(i-ii)) 12S = 0 ---> S=0

i-(ii-iii)) 12J = 24 ---> J=2

i(J replaced with 2)) (6 * 2) + 6P = 36 ---> P=4

i finally got it thanks to you. im astonished how unintuitive the solution to such a seemingly easy riddle is.

>>358658

Or like that.
That is just a different way of solving the system. There are always several waysYou just took more steps.