SOLUTION: What is in verse of the coefficient matrix of the equivalent matrix equation Please help me solve this equation : x-6y=5 -x+4y=-5

Here's one exactly like it.  Use it as a guide.
Do the same things all the way through.  Just
use your numbers instead:

7x - 8y = -21
 x -  y = -2


Write the system as:




Then write that as:



Now we must find the inverse of the 2x2 
coefficient matrix 

To find the inverse matrix of a 2x2 matrix:



1.  Find the value of its determinant:



2.  Swap the upper left and lower right elements of :



3. Change the sign of the upper right and lower left elements.



4. Divide every element by the value of the determinant found
   in step 1.





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Next we left-multiply both sides of the equation



by the inverse 

and we get:

 

Next we multiply the first two matrices on the left:

 

Simplifying,





Now multiply the two matrices on the left:



Simplifying:



Now multiply the two matrices on the right:



Simplifying





So the solution is;  ,

Edwin