SOLUTION: 5x-6y+4z=15, 7x+4y-3z=19, 2x+y+6z=46 sove using cramer rule.

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Question 1004053: 5x-6y+4z=15,
7x+4y-3z=19,
2x+y+6z=46
sove using cramer rule.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
5x-6y+4z=15,
7x+4y-3z=19,
2x+y+6z=46
solve using cramers rule
 
Write in the 1 coefficient:



Cramer's rule:
 
There are 4 columns,
 
1. The column of x-coefficients matrix%283%2C1%2C5%2C7%2C2%29
 
2. The column of y-coefficients matrix%283%2C1%2C-6%2C4%2C1%29
 
3. The column of z-coefficients matrix%283%2C1%2C4%2C-3%2C6%29 
 
4. The column of constants:     red%28matrix%283%2C1%2C15%2C19%2C46%29%29
 
There are four determinants:
 
1. The determinant D consists of just the three columns
of x, y, and z coefficients. in that order, but does not
contain the column of constants.
 
D=abs%28matrix%283%2C3%2C5%2C-6%2C4%2C7%2C4%2C-3%2C2%2C1%2C6%29%29. 
 
It has value D=419.  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 D%5Bx%5D is like the determinant D
except that the column of x-coefficients is replaced by the
column of constants.  D%5Bx%5D does not contain the column 
of x-coefficients.
 
.
 
It has value D%5Bx%5D=1257.
 
3. The determinant D%5By%5D is like the determinant D
except that the column of y-coefficients is replaced by the
column of constants.  D%5By%5D does not contain the column 
of y-coefficients.
 
.
 
It has value D%5By%5D=1676.
 
4. The determinant D%5Bz%5D is like the determinant D
except that the column of z-coefficients is replaced by the
column of constants.  D%5Bz%5D does not contain the column 
of z-coefficients.
 
.
 
It has value D%5Bz%5D=2514.
 
Now the formulas for x, y and z are
 
x=D%5Bx%5D%2FD=1257%2F419=3
y=D%5By%5D%2FD=1676%2F419=4
x=D%5Bz%5D%2FD=2514%2F419=6
 
Edwin