Why do it the hard way?
Add the two equations to get
7x = -14
x = -2
y = (-4 -3x)/2 = 1
To apply the Gauss-Jordan method, read this:
http://mathrefresher.blogspot.com/2007/04/gauss-jordan-elimination.html
It seems like a waste of time to me.
Use Gauss-Jordan to solve
3x + 2y = -4
4x – 2y = -10
2 answers
3x+4y=38
5x-5y=-30
5x-5y=-30