We need to end up with a matrix that looks like this:



Plan: by using row operations,

1. get a 0 on the left of the 2nd row.
2. get a 0 in the middle in the 1st row.
3. get a 1 on the left of the 1st row.
4. get a 1 in the middle of the 2nd row.

Also, any time a row can be easily divided through
by a constant, we will stop and do that too:

To get a 0 where the 3 is, we mentally multiply
each member of the first row by -3 and mentally
add it to 5 time the corresponding number and
replace the number in the second row by what
we get.  To make it easy to do this mentally,
be sure to write -3 to the left of the 1st row
and 5 to the left ofthe 2nd row, so we can
easily do the work mentally:

 



Notice that the second row can be divided through by -13,
so we stop and do that:



To get a 0 where the 1 in the middle on the top
row is, we mentally multiply each member of the 
2nd row by -1 and mentally add it to 1 times the 
corresponding number and replace the number in 
the first row by what we get.  To make it easy 
to do this mentally, be sure to write -1 to the 
left of the 2nd row and 1 to the left of the 1st
row, so we can easily do the work mentally:


 


Now we just need to get a 1 where the 5 is. So
we divide the 1st row through by 5:



Now we interpret the matrix



as the sytem of equations:



or just



Edwin