Question 150001
I don't know how to make matrices here, but I'll try. 

[ 4  -2 | 3 ]
[-2  3  | 1 ] <-- That's your augmented matrix representing the system of equations. 

Now row one column one has to be a pivot, so row two column one must become zero. 
Add 1/2*row one to row two. 

[4   -2 | 3] 
[0   2  | 5/2] 

So you have it in the proper inverted triangle form now. Equate the components. 

{{{2y = 5/2}}} 
{{{y = 5/4}}} 

Substitute this back into: 

{{{4x - 2y = 3}}} 
{{{4x - 2(5/4) = 3}}} 
{{{4x - 5/2 = 3}}} 
{{{4x = 3 + 5/2 = 11/2}}} 
{{{x = 11/8}}} 

So there is the solution: <b>(11/8, 5,4)</b>

-ntnk