There is no EASY way to do this problem (and that is why computers were invented, because computers do this so easily!)
First, let me say that there are methods using matrices to do this problem a little more easily, but inverting a 5x5 general matrix is NOT easy! Nor is the use of a 5x5 determinant.
However, I can get you started.
Write the equations in matrix form as follows
a b c d e f
1 1 0 0 0 -4
0 1 1 0 0 -2
6 3 1 1 0 -26
0 3 3 1 1 -8
9 0 3 0 1 44
The object of the game is to isolate variables by arithmetic operations on the lines, including the constants on the right.
Start out by subtracting 6 * line 1 from line 3 and 9 * line 1 from line 5.
Use the 2 equation (2nd line) to make the first non-zero coefficient in lines 3, 4, and 5 = 0 by adding or subtracting multiples of line 2.
Make the first coefficient in line 3 = 1 by division and then make the first non-zero coefficient in lines 4 and 5 by adding or subtracting multiples of line 3.
This will leave you with a 2 by system in d and e which you can solve easily.
The plug the values back into the equations above to get the values of a, b and c.
This is a MESSY process and it must be done carefully because arithmetic mistakes will kill you. I am sorry I cant make this easier for you.
