SOLUTION: x+y+z=6 2x-y+z=3 x+2y-3z=-4 solve using cramers rule

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Question 355223: x+y+z=6
2x-y+z=3
x+2y-3z=-4
solve using cramers rule

Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
x+y+z=6
2x-y+z=3
x+2y-3z=-4
------------
You can check your answers.
x = 1
y = 2
z = 3

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
x+y+z=6
2x-y+z=3
x+2y-3z=-4
solve using cramers rule



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, post again asking how. 
 
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


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