Question

Solve the system of equation x+3y+2z ,2x-y+3z,3x-5y+4z,x+17y+4x

Answer 1

Answer:

// Solve equation [4] for the variable  x 

 

[4] x = -17y - 4z

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

  [1] (-17y-4z) + 3y + 2z = 0   [1] - 14y - 2z = 0

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

  [2] 2•(-17y-4z) - y + 3z = 0   [2] - 35y - 5z = 0

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

  [3] 3•(-17y-4z) - 5y + 4z = 0   [3] - 56y - 8z = 0

// Solve equation [3] for the variable  z 

 

[3] 8z = -56y [3] z = -7y

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

  [1] - 14y - 2•(-7y) = 0   [1] 0 = 0 => Infinitely many solutions