Solve the system of equations.

2x+4y+3z=6
5x+8y+6z=4
4x+5y+2z=6

A. (x=-7, y=9, z=-7)
B. (x=-8, y=10, z=-6)
C. (x=-9, y=11, z=-5)
D. (x=-6, y=8, z=-4)

( choice B )  { x , y , z } = { -8 , 10 , -6 }

Step-by-step explanation:

* System of Linear Equations entered :

  [1]    2x + 4y + 3z = 6

  [2]    5x + 8y + 6z = 4

  [3]    4x + 5y + 2z = 6

* Solve by Substitution :

// Solve equation [3] for the variable  z  

 [3]    2z = -4x - 5y + 6

 [3]    z = -2x - 5y/2 + 3

// Plug this in for variable  z  in equation [1]

  [1]    2x + 4y + 3•(-2x-5y/2+3) = 6

  [1]    -4x - 7y/2 = -3

  [1]    -8x - 7y = -6

// Plug this in for variable  z  in equation [2]

  [2]    5x + 8y + 6•(-2x-5y/2+3) = 4

  [2]    -7x - 7y = -14

// Solve equation [2] for the variable  y  

 [2]    7y = -7x + 14

 [2]    y = -x + 2

// Plug this in for variable  y  in equation [1]

  [1]    -8x - 7•(-x +2) = -6

  [1]    -x = 8

// Solve equation [1] for the variable  x  

  [1]    x = - 8  

// By now we know this much :

   x = -8

   y = -x+2

   z = -2x-5y/2+3

// Use the  x  value to solve for  y  

   y = -(-8)+2 = 10  

// Use the  x  and  y  values to solve for  z  

 z = -2(-8)-(5/2)(10)+3 = -6

answer:

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