SOLUTION: how do I solve this system using Cramer's Rule? -3x+4y-z=-1 5x-2y+3z=-1 -x+3y-4z=-22

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Question 784631: how do I solve this system using Cramer's Rule?
-3x+4y-z=-1
5x-2y+3z=-1
-x+3y-4z=-22

Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Calculate the determinant consisting of the coefficients on the variables. Call that . Replace the -column of the determinant with the values in the constant column. Calculate this determinant and call it . Replace the column and calculate and the column and call it , then







John

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Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
-3x+4y-z=-1
5x-2y+3z=-1
-x+3y-4z=-22
Line up the letters and
show all coefficients:

-3x + 4y - 1z =  -1
 5x - 2y + 3z =  -1
-1x + 3y - 4z = -22

To solve using 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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