Question 164544
The Gauss-Jordan solutions were generated by the <a href="http://www.math.odu.edu/~bogacki/lat/"> Linear Algebra Toolkit</a>



# 1


The system 


{{{system(x+y=2,7x+8y=21)}}}



translates to the matrix 



{{{(matrix(2,3,1,1,2,7,8,21))}}}




Gauss-Jordan Method:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/gaus_jordan.png" alt="Photobucket - Video and Image Hosting">



So the solution is {{{x=-5}}} and {{{y=7}}} (these are the values in the right most column of the last step)



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# 2



The system 


{{{system(x-y+3z=6,x-2y=5,2x-2y+5z=9)}}}



translates to the matrix 



{{{(matrix(3,4,1,-1,3,6,1,-2,0,5,2,-2,5,9))}}}




Gauss-Jordan Method:



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/gaus_jordan2.png" alt="Photobucket - Video and Image Hosting">




So the solution is {{{x=-11}}}, {{{y=-8}}}, and {{{z=3}}} (these are the values in the right most column of the last step)