use cramer's rule to solve the system

[kayesal]

-4x+3y+2z=29
3y-3z=6
-3x-2z=-23

 

[stapel]

Cramer's Rule is fairly formulaic. Where are you stuck in the plug-n-chug process?

Please reply showing all of your steps. Thank you.

Eliz.

 

[kayesal]

Use Cramer's rule to solve

-4x + 3y + 2z =  29
      3y - 3z =   6
-3x       -2z = -23

D =  -4  3  2
      0  3 -3   = -4(3x-20-0x-3)-(0)+(-3)(3x-3)-(3x2)  = 69
     -3  0 -2

Dx =  29  3  2
       6  3 -3   = -29(3 x -2) -(0x-3)-6(3x-2) + -23(3x2)-(3 x -3)  = 207
      -3  0 -2  


Dy =  -4 29  2
       6  3 -3   = -4 (29x-3)-(6x2) - 0(29x2) - (-23 x-2) +3(29x-3) -(6 x2)= 27

( which does not divide evenly by 69)  so either I have an error in the matrix set up or the math?)

Dz = -4  3  29
      0  3   6    = (-4)(3x-23)-(0x6) - (0)+(-3)(3 x 6) - (3 x 29) =483

D=69

Dx = 207/69 = 3
Dy = 27/69...?
Dz 483/69 = 7

-3   0 -23
 3 -23  -2

______________
stapel - edited for readability.

 

[stapel]

Why do D_y and D_z have only two rows? What is the meaning of the two rows of digits at the end of your post?

What sort of formula have you been taught for computing determinants? Because I have never seen the computation of a numerical determinant that involved all those variables: "-29(3x - 2) - (0x - 3) - 6(3x - 2) + -23(3x2) - (3x - 3)", etc.

Why would it be a problem if the value of D does not evenly divide into the value of D_x, D_y, or D_z?

By the way, your values for D, D_x, and D_z are correct.

Eliz.