This is really the matrix abbreviation for the system of equtions:  





Now we need to find the inverse of the coefficient matrix



To find the inverse of a 2x2 matrix:

1. Interchange the upper left and lower right elements:



2. Multiply the upper right and lower left elements by -1:



3. Find the determinant of this matrix:



4. Divide every element of  by this value:



That is the inverse of the coefficient matrix.

Left-multiply both sides of the matrix
equation:



by the inverse of the coefficient matrix:



Since matrix multiplication is associative, we can move
the parentheses from around the 2nd and 3rd matrices
on the left to around the 1st and 2nd matrices on the
left:



Now we multiply the two matrices on the far
left and the far right:  



Simplify:







Multiply the matrices on the left:

 

Simplify:

 

So the solution is 

, 

Edwin