find the following lonear equqtion by mtrix method

12p+4q+17r+11s=5
14p+8q+9r+4s=8
3p+7q+2r+5s=12
5p+12q+9r+7s=7

set up the 4by4 matrix of the coefficients.

find the inverse of that matrix
multiply that inverse matrix by
5
8
12
7

This will take several sheets of paper and lots of patience
- not really suitable to write up in this format, matrices are horrible to type in jiskha.
There are several good webpages that will find the inverse of any square matrix, if it exists.
Just google it.