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):
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
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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
