Question

solve the system of equations 4x+2y+z+w=0,6x+3y+4z+7w=0,2x+y+w=0

Answer 1

System of Linear Equations entered :

  [1]    4x + 2y + z + 3w = 0

  [2]    6x + 3y + 4z + 7w = 0

  [3]    2x + y + w = 0

Solve by Substitution :

Solve equation [3] for the variable  w  

  [3]    w = -2x - y  

 Plug this in for variable  w  in equation [1]

   [1]    4x + 2y + z + 3 x (-2x-y ) = 0

  [1]    -2x - y + z = 0

Plug this in for variable  w  in equation [2]

 [2]    6x + 3y + 4z + 7 x (-2x-y ) = 0

[2]    -8x - 4y + 4z = 0

Plug this in for variable  w  in equation [3]

 [3]    2x + y + (-2x-y ) = 0

[3]    0 = 0 =>  Infinitely many solutions  

THEREFORE, THERE ARE INFINETLY MANY SOLUTIONS.