SOLUTION: Use the Cramer’s rule to solve the following system of linear equations; x - y + z = 8, 2x + 3y - z = -2, . 3x - 2y - 9z = 9

Write in all the 1 and -1 coefficients:



Cramer's rule:
 
There are 4 columns,
 
1. The column of x-coefficients 
 
2. The column of y-coefficients 
 
3. The column of z-coefficients  
 
4. The column of constants:     
 
There are four determinants:
 
1. The determinant  consists of just the three columns
of x, y, and z coefficients. in that order, but does not
contain the column of constants.
 
. 
 
It has value .  I'm assuming you know how to find the
value of a 3x3 determinant, for that's a subject all by itself.
If you don't know how, let me know in the message form below and
I'll get back to you by email.  There is never any charge as I
am a retired math professor just doing this for fun! :) 
 
2. The determinant  is like the determinant 
except that the column of x-coefficients is replaced by the
column of constants.   does not contain the column 
of x-coefficients.
 
.
 
It has value .
 
3. The determinant  is like the determinant 
except that the column of y-coefficients is replaced by the
column of constants.   does not contain the column 
of y-coefficients.
 
.
 
It has value .
 
4. The determinant  is like the determinant 
except that the column of z-coefficients is replaced by the
column of constants.   does not contain the column 
of z-coefficients.
 
.
 
It has value .
 
Now the formulas for x, y and z are
 



 
Edwin