Expert: Sherman D. - 5/3/2005

Question
I have THREE problems, with FOUR unknowns in each, is there any way I can solve them , I assume I may get more than one set of possible answers, can anyone help?

6s + 6d + 9a + 10p = 20

10s + 9d + 5a + 6p = 30

16s + 15d + 14a + 16p = 50

Do I need to create a Matrix to solve this?  This is not a homework assignment, I am trying to see how certain game figures are rated in a minature game and I can't make heads or tails of it!

Thanks
jojomanzo@gmail.com

Answer
In short, this problem has infinite possibilities.

6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50

most of them if you have 4 unknowns, you have 4 rows.

6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30

Multiply top by 5 and bottom by -3

30s + 30d + 45a + 50p = 100
-30s - 27d - 15a - 18p = -90

3d + 30a + 32p = 10

10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50

Multiply top by 8 and bottom by -5

80s + 72d + 40a + 48p = 240
-80s - 75d - 70a - 80p = -250

-3d - 30a - 32p = -10

so this gives you


3d + 30a + 32p = 10
-3d - 30a - 32p = -10

as you can see the top and bottom cancel each other out.

6s + 6d + 9a + 10p = 20
16s + 15d + 14a + 16p = 50

Multipl top by 8 and bottom by -3

48s + 48d + 72a + 80p = 160
-48s - 45d - 42a - 48p = -150

3d + 30a + 32p = 10

so this gives you

3d + 30a + 32p = 10
-3d - 30a - 32p = -10

top and bottom cancel each other out.