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
