Question 249045
Step 1) Convert the system 


{{{system(x+y=1,4x-3y=11)}}}



into the augmented matrix



{{{(matrix(2,3,1,1,1,4,-3,11))}}}



Take note that the coefficients form the first 2x2 block and the right hand values form the last column. Visually, the correspondence is



{{{system(highlight_green(1)*x+highlight_green(1)*y=highlight(1),highlight_green(4)*x+highlight_green(-3)*y=highlight(11))}}} ----> {{{(matrix(2,3,highlight_green(1),highlight_green(1),highlight(1),highlight_green(4),highlight_green(-3),highlight(11)))}}}


This conversion of notation allows us to ignore the variables (for now) since everything is based off of the numerical coefficients and right hand values.



Step 2) Row Reduction


Our next step is to row reduce the matrix {{{(matrix(2,3,1,1,1,4,-3,11))}}} into row reduced echelon form (rref form). (Note: Solution provided by the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>)


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rref1-2.png">


Looking at the last matrix {{{(matrix(2,3,1,0,2,0,1,-1))}}}, the last column has the values 2 and -1 in it. So this means that the solution is {{{x=2}}} and {{{y=-1}}} forming the ordered pair (2,-1).