We will start with the system of equations first because it uses
that very matrix:

Both equations of



can be divided through by 2, and the system becomes



Abbreviate the above system by the AX=B form:



Now we need to find the inverse of the coefficient matrix, which
is the very matrix you were asked to find the inverse of:



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:



5. Simplify



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 move
the parentheses:



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