Question

What is the solution to the following system 4x+3y-z=-6

Answer 1

Solve equation [2] for the variable  y  
 

[2] y = 6x + 3z - 12

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

  [1] 4x + 3•(6x+3z-12) - z = -6   [1] 22x + 8z = 30

// Plug this in for variable  y  in equation [3]

  [3] 8x + 2•(6x+3z-12) + 4z = 6   [3] 20x + 10z = 30

// Solve equation [3] for the variable  z  
 

[3] 10z = -20x + 30 [3] z = -2x + 3

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

  [1] 22x + 8•(-2x+3) = 30   [1] 6x = 6

// Solve equation [1] for the variable  x  

  [1] 6x = 6    [1] x = 1 

// By now we know this much :

  x = 1   y = 6x+3z-12   z = -2x+3

// Use the  x  value to solve for  z  

  z = -2(1)+3 = 1 

// Use the  x  and  z  values to solve for  y  
  y = 6(1)+3(1)-12 = -3 

Solution : {x,y,z} = {1,-3,1}