Is this the best way to solve 2 x 2 systems?

Definitely NO!

But, if you've got a computer (or a graphing calculator) to pop the inverses, it's a pretty slick way to solve 3 x 3's and up.

There's one more important thing that I need to tell you about inverse functions...  It will make more sense now that you know about using them to solve systems.

If the determinant of a matrix is zero,
then the matrix does NOT have an inverse matrix!

Check it out:

A = [ row 1: 1 , 3  row 2: 2 , 6 ]

 

det A = [ row 1: 1 , 3  row 2: 2 , 6 ]


= ( 1 )( 6 ) - ( 2 )( 3 ) = 0