# Thread: finding equation for 4 variable system

1. ## finding equation for 4 variable system

Hi all,

I am struggling with a Problem at the momment,

ax + by + cz = e

I have a data set of "e" to "x" ,"y","z", and would like to get a possible range of the constants "a","b","c" .

data set eg.

e - x - y - z
6 - 11 - 1713 - 54
4 - 11 - 1123 - 25
2 - 9 - 1546 - 64
1 - 10- 789 - 87

the idea is to have an equation where x,y,z are entered and e is aquired.

Any help will be much appriciated.

Thanks
jonod

2. Hello, jonod!

Determine the equation: .$\displaystyle ax + by + cz \:= \:e$

which satisfies these data:

. . $\displaystyle \begin{array}{ccc|c} x & y & z & e \\ \hline 11 & 1713 & 54 & 6 \\ 11 & 1123 & 25 & 4 \\ 9 & 1546 & 64 & 2 \\ 10 & 789 & 87 & 1 \end{array}$

We have a system of equations: .$\displaystyle \begin{array}{ccc} 11a + 1713b + 54c &=& 6 \\ 11a + 1123b + 25c &=& 4 \\ 9a + 1546b + 64c &=& 2 \\ 10a + 789b + 87c &=& 1 \end{array}$

If we're lucky, it has a solution . . .