Question 107383
Start with the given system


5x+2y=2
3x-y=-12



Now write the coefficients and the right side in an augmented matrix:

{{{(matrix(2,3,5,2,2,3,-1,-12))}}}



Multiply Row 1 by {{{1/5}}} to make the pivot 1:


{{{(matrix(2,3,1,2/5,2/5,3,-1,-12))}}}


 Add  -3*Row 1 to Row 2 to get the new Row 2


{{{(matrix(2,3,1,2/5,2/5,0,-11/5,-66/5))}}}


Multiply Row 2 by {{{-5/11}}} to make the pivot 1:


{{{(matrix(2,3,1,2/5,2/5,0,1,6))}}}


 Add  -2/5*Row 2 to Row 1 to get the new Row 1

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



The matrix is now in <font size=4><b>reduced row echelon form</b></font>



So our answer is (-2,6) or {{{x=-2}}}, {{{y=6}}}



If you need more help with row reduction, check out the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>