Question 146738
If you started with:
  3x + 4y = 11
   x + 3y  = 2
.
The "coefficient matrix" is:
3 4
1 3
.
The determinant of the "coefficient matrix" is:
(3*3) - (1*4) = 9 -4 = 5
.
The 'x' matrix is:
11 4
 2 3
.
The determinant of the 'x' matrix is:
(11*3)-(2*4) = 33 -8 = 25
.
The 'y' matrix is:
3 11
1  2
.
The determinant of the 'y' matrix is:
(2*3)-(1*11) = 6 -11 = -5
.
Solution for 'x' is "det of x"/"det of coefficient":
25/5 = 5 
.
Solution for 'y' is "det of y"/"det of coefficient":
-5/5 = -1
.
Our solution is (x,y) = (5,-1)
.
To check, plug it back into:
   x + 3y  = 2
   5 + 3(-1)  = 2
   5 - 3  = 2
       2 = 2 (check)
and
  3x + 4y = 11
  3(5) + 4(-1) = 11
  15 - 4 = 11
       11 = 11 (check)