see below the picture for an explanation of what was done.
step 1 is your original equation.
step 2 creates your augmented matrix which includes the coefficients of the x and y terms plus the constant term on the right.
step 3 adds row 2 plus 3 * row 1 together and puts the result in row 2.
step 4 shows you the result after performing the operation in step 3.
the result of that operation is to make the number in column 1 row 2 equal to 0.
step 5 multiplies row 2 * -1/7 and puts the result in row 2.
step 6 shows you the result after performing the operation in step 5.
the result of that operation is to make the number in column 2 row 2 equal to 1.
step 7 adds row 1 + 4 * row 2 together and puts the result in row 1.
step 8 shows you the result of the operation in step 7.
the result of that operation is to make the number in column 2 row 1 equal to 0.
your matrix is now in the reduced form required by the gauss-jordan method.
all the coefficients are equal to 1.
row 1 has a coefficient of 1 in column 1 and a 0 in all other coefficient columns (only 2 columns in this problem).
row 2 has a coefficient of 1 in column 2 and a 0 in all other coefficient columns (only 2 columns in this problem).
once you get the matrix in this form, your solution is read off as:
x = 3
y = 2
you can confirm this solution is good by replacing x and y in the original equation and you'll see that both equations are true.
in step 3, i showed R2 = R2 + 3R1.
i could also have shown it as R2 + 3R1 -> R2
same with step 5 and step 7.
step 5 could have been shown as -1/7 * R2 -> R2
step 7 could have been shown as R1 + 4R2 -> R1
check out the following video:
http://www.youtube.com/watch?v=CsTOUbeMPUo
partickJMT goes fairly quickly, but his method is clear.
pause the video and you can even go back to wherever you want to start again by clicking on the video progress indicator bar, if you get lost or want to see parts of the video again.
the method is consistent to what I showed you, except that his example is a little more complex, which is good because you will eventually get to those more complex examples in your studies soon enough.
there is also a nice little calculator on the internet that you can use to check out your solution.
that calculator can be found at the following link:
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
the result of using that calculator is shown below:
