Hi again!

So even though I more or less know how to solve a system of linear equations, I still can't help keep getting lost whenever things get more complicated.

For example, I've got this linear system that I can't seem to solve even though the end result is supposed to be rather simple. So, I've got this linear system:

|2x_{1}+ x_{2}- 5x_{3 }+ x_{4 }= 8

|x_{1}- 3x_{2}+ 0x_{3 }-6x_{4 }= 9

|0x_{1 }+ 2x_{2 }- x_{3 }+ 2x_{4}= -5

|x_{1 }+ 4x_{2 }-7x_{3 }+ 6x_{4 }= 0

And so, using the coefficients, you get this coefficient matrix:

2 1 -5 1 | 8

1 -3 0 -6 | 9

0 2 -1 2 | -5

1 4 -7 6 | 0

Anyone care to help from here on? I've certainly tried, but my level of maths isn't enough to get an answer out of that.