Solve Using Cramer's Rule

 x + 2y =  5
2x -  y = -3

Note they are lined up vertically: x under x, y under y,
sign under sign, = under =, and constant under constant. 

Give the x in the first equation a 1 coefficient.
Give the y in the first equation a -1 coefficient.

1x + 2y =  5
2x - 1y = -3

Make a determinant D, with the coefficients of x and y,
in the same order as they appear

D =  |1  2|
     |2 -1|

Evaluate it by cross-multiplying (1)(-1) - (2)(2) 
= -1-4 = -5

So D = -5

Make a determinant Dx, with the right column the same
as the right column of D, but with the column of
constants replacing the FIRST COLUMN 

Dx = | 5  2|
     |-3 -1|

Evaluate it by cross-multiplying (5)(-1) - (2)(-3) 
= -5+6 = 1

So Dx = 1

Make a determinant Dy, with the left column the same
as the left column of D, but with the column of
constants replacing the SECOND COLUMN 

Dy = |1  5|
     |2 -3|

Evaluate it by cross-multiplying (1)(-3) - (5)(2) =
-3-10 = -13

So Dy = -13

Now  x = Dx/D = 1/-5 = -1/5 = -.2, and 
y = Dy/D = -13/-5 = 13/5 = 2.6

Edwin