How do you solve using gaussian elimination or gauss-jordan elimination, #x+2y=7# , #3x-2y=-3#?
Rewrite this system in matrix form
Now we want to put this matrix in triangular form. This amounts to eliminating y for instance.
Adding both rows yields
[1 2] [x] = 
[4 0] [y] 
In this form, you see that triangular means one equation will have all zero matrix element except one. In our case the bottom equation reads
The equation right above will have two non-zero matrix elements. Using the solution from the bottom equation, you can plug this solution into the equation above to get
That method only becomes efficient when you have more than two variables.