Solve the following matrix
[ 2 8 22 ]
[ 4 1 14 ]
I think you need to multiply the top by negative 2 and then subtract from the bottom. but I am confused from there.
2x + 8y = 22
4x + y = 14
[ 2 8 22]
[ 4 1 14]
After this however I am lost.
You have to end up with a matrix that
looks like this:
[ 1 0 #]
[ 0 1 #]
Then the solutions for x and y will appear
where the #'s are.
We get the 0's first, then we get the 1's:
Your augmented matrix is:
[ 2 8 22]
[ 4 1 14]
Get a 0 where the 4 is:
Multiply the top row through by -2
[-4 -16 -44]
[ 4 1 14]
Add the top row to the bottom row but
leave the top row as it is:
[-4 -16 -44]
[ 0 -15 -30]
Let's stop and simplify by dividing the
top row through by -4, and the bottom row
through by -15
[ 1 4 11]
[ 0 1 2]
Get a 0 where the 4 is:
Multiply the bottom row by -4:
[ 1 4 11]
[ 0 -4 -8]
Add the bottom row to the top row but keep
the bottom row as it is.
[ 1 0 3]
[ 0 -4 -8]
Get a 1 where the -4 is by dividing the
bottom row through by -4
[ 1 0 3]
[ 0 1 2]
The two numbers in the right-most column 
are the answers:
x = 3, and y = 2
Edwin
