Cramer's Rule!

Well, here goes the first blog of the HOLIDAYSSSS! :)

x=Dx/D y=Dy/D z=Dz/D

Where D is the determinant of the coefficient matrix.

Used to solve systems of equations using matrices and determinants.

Example 1:
Solve each system of equations by using Cramer's Rule.
5x-4y=1
3x+2y=5
D=5 -4 =22 Dx=1 -4 =22 Dy=5 1 =22
3 2 5 2 3 5
x=22/22=1 y=22/22=1
(1,1)

Example 2:
Solve each system of equations by using Cramer's Rule.
5x-2y=11
x+3y=9
D=5 -2 =17 Dx=11 -2 =51 Dy=5 11 =34
1 3 9 3 1 9
x=51/17=3 y=34/17=2
(3,2)

Example 3:
Solve each system of equations by using Cramer's Rule.
3x+2y=-1
2x-y=4
D=3 2 =-7 Dx=-1 2 =-7 Dy=3 -1 =14
2 -1 4 -1 2 4
x=-7/-7=1 y=14/-7=-2
(1,-2)

Example 4:
Solve each system of equations by using Cramer's Rule.
7x+y=7
-x+2y=14
D=7 1 =15 Dx=7 1 =0 Dy=7 7 =105
-1 2 14 2 -1 14
x=0/15=0 y=105/15=7
(0,7)

Example 5:
Solve each system of equations using Cramer's Rule.
x-2y+3z=2
2x-3y+z=1
3x-y+2z=9
D= 1 -2 3 =18 Dx= 2 -2 3 =54 Dy= 1 2 3 =36 Dz= 1 -2 2 =18
2 -3 1 1 -3 1 2 1 1 2 -3 1
3 -1 2 9 -1 2 3 9 2 3 -1 9
x=54/18=3 y=36/15=2 z=18/18=1
(3,2,1)

&&& of course my matrices WOULD mess up once again.. I still don't know how to fix themmmm :(