123
of 3

Cramer's Rule for 3x3's

For

 Dx :
| row 1: 2 , -1 , 6 row 2: -3 , 4 , -5 row 3: 8 , -7 , -9 |

and delete the column with the x guys...

 | row 1: __ , -1 , 6 row 2: __ , 4 , -5 row 3: __ , -7 , -9 | ... delete the x guys (column 1)

Replace that column with the "= guys" and start crunching!

Dx = | row 1: 10 , -1 , 6 row 2: 11 , 4 , -5 row 3: 12 , -7 , -9 | = -1499
 

So, x = ( Dx / D ) = ( -1499 / -141 ) = ( 1499 / 141 )
 

For

 Dy :

Do the same kind of thing...

Take D again...

| row 1: 2 , -1 , 6 row 2: -3 , 4 , -5 row 3: 8 , -7 , -9 |

and delete the column with the y guys...

 | row 1: 2 , __ , 6 row 2: -3 , __ , -5 row 3: 8 , __ , -9 | ... delete the y guys (column 2)

Replace that column with the "= guys" and crunch!

Dy = | row 1: 2 , 10 , 6 row 2: -3 , 11 , -5 row 3: 8 , 12 , -9 | = -1492
 

So, y = ( Dy / D ) = ( -1492 / -141 ) = ( 1492 / 141 )