Math algebra questions help please?

Question

how do you solve this questions?

3x - 9y + 7 = -21
-4x + 5y - 2z = 5
-11x + y + 12z = -53

Answer 1

     3 x -9 y + 7  =  - 21            ->  ( 1 )

    - 4 x + 5 y  - 2 z  = 5           ->  ( 2 )

     - 11x + y + 12 z  = - 53   ->   ( 3 )

    Multiply  equation  ( 2 )   by   6

   ( -4x + 5y - 2 z  = 5 )  6

    - 24 x  + 30 y  - 12 z  = 3 0    ->  (  4 )

      Add  equation  (  4 ) &  ( 3 )

    -  24 x +  30 y  - 12 z  = 30

    - 11x  +  y  + 12 z   =  - 53

_________________________

  - 35 x + 31 y    =  - 23        ->  ( 5 )

 Multiply   equation  ( 1 )   by   35   &   ( 5 )  by   3

    ( 3x  - 9y  =  - 28  ) 35       ->  ( 6 )

    ( - 35 x + 31y  = - 23 )  3   ->  (  7 )

   Add   equation   ( 6 ) & ( 7 )

   105 x  - 315 y  =  - 980

  - 105 x + 93 y  = -69

____________________

           - 222 y  =  - 1049

 

             y  =  1049/  222

Substitute  the  y  value  in   equation  ( 1)

      3 x  =  -28 + 9 (  1049 / 222 )

     3 x =  -28 ( 222 ) + 9 ( 1049 ) / 222

           =  - 6216 + 9441 / 222

     Therefore  x  =  3225 / 222 x 3

                        x  =  1075 / 222

     Therefore  x =  1075 / 222 ,  y =  1049 / 222

   Substitute  the  values  in  equation  ( 2 )

   2 z  =  5 + 4 (  1075 / 222 ) - 5 (  1049 / 222 )

   2z  =  5 + {(  4300 )  - (  5245 )} / 222

   2z  = {5 ( 222 )  + 4300 - 5245}/222

         =  {1110 + 4300 - 5245}/222

         =  (5410 - 5245)/222 = 165/222

  Therefore  z  =  165 / 444

    The  values  of  x =  1075 / 222 , y =   1049 / 222 , z = 165 / 444.

Comments

x and y values are correct but z value is wrong. check the sign error in second equation.

Second equation simplifies to z = 1/2( -5 - 4x + 5y)

If you substitute x and y values in second equation the result will be z = - 55/148

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Solve the second equation 2 : - 4x + 5y - 2z = 5 for z.

Add (4x - 5y) to each side.

- 4x + 5y - 2z + (4x - 5y) = 5 + (4x - 5y)

- 2z = 5 + 4x - 5y

Divide each side by negative 2.

(- 2z)/(- 2) = (5 + 4x - 5y)/(- 2)

z = (5)/(- 2) + (4x)/(- 2) - (5y)/(- 2)

z = - 5/2 - 2x + 5y/2

Substitute the value of x =  1075 / 222 and y =   1049 / 222 in the above equation.

z = - 5/2 - 2(1075 / 222) + [ 5(1049 / 222) ]/2

z = - 5/2 - 2150 / 222 + [5245 / 444]

Least common factor of 2, 222 and 444 is 444.

z = [ (- 5)(222) - (2150)(2) + 5245] / 444

z = [ - 1110 - 4300 + 5245 ] / 444

z = - 165 / 444

z = - (3*55) / (3*148)

z = -  55/148.