SOLUTION: Hello, I am to use Cramers rule to solve the system: x -z=4 6y-z=-19 2x+3y=1 Find the determinates: D= Dx= Dy= Dz= I can't figure it out. Thank you

Question 1043605: Hello,

I am to use Cramers rule to solve the system:

x -z=4
6y-z=-19
2x+3y=1
Find the determinates:
D=
Dx=
Dy=
Dz=
I can't figure it out.
Thank you so much
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I am to use Cramers rule to solve the system:
x -z=4
6y-z=-19
2x+3y=1
Find the determinates [sic]:
----

|1 0 -1 4|
|0 6 -1 -19|
|2 3 0 1|

==============
Det = 1*(6*0 - 3*-1) - 0*() - 1*(0*3 - 2*6) = 3 + 12 = 15
----
Dx = 0*() + 1*(6*1 - 3*-19) + 4*(6*0 - 3*-1) = 63 + 12 = 75
----
-Dy = 1*(-1) +1*(0+38) + 4*(0+2) = -1 + 38 + 8 = 45
----
Dz = 1*(6*1 - 3*-19) - 0*() + 4*(0 - 2*6) = 63 -48 = 15
---
x = 5
y = -3
z = 1
-----------
It's tedious and you have to be careful, but not hard.

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
About the Cramer's rule and how it works see the lessons
    - Determinant of a 3x3 matrix
    - Co-factoring the determinant of a 3x3 matrix
    - HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)
    - Solving systems of linear equations in three unknowns using determinant (Cramer's rule)
    - Solving word problems by reducing to systems of linear equations in three unknowns
in this site.

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