How would you solve a system of linear equations using C programming?

The equations are like this:

3a +4b +6c +7d....=34

4a +6b +3c +8d....=26

2a +2b +9c +2d....=84

..............................

Basically, you have 'x' many variables and 'x' many equations, where 'x' is a variable number. I tried converting the system of equations into matrices, like this:

[3, 4, 6, 7,...]______[a]_______[34]

[4, 6, 3, 8,...]_X____[b]____=__[26]

[2, 2, 9, 2,...]______[c]_______[84]

[................]______[...]______[...]

But I have no idea what to do now. I tried looking it up online, and found something called Gaussian Elimination, which seems to be able to solve these types of problems, but I have no idea how it works or how to code it.