If x = a , y = b , z = c is a solution of the system of linear equations x + 8 y + 7 z = 0 9 x + 2 y + 3 z = 0 x + y + z = 0 Such that the point a , b , c lies on the plane x + 2 y + z = 6 , then 2 a + b + c equals:

Step-by-step solution

x + 8 y + 7 z = 0     . . . i                 9 x + 2 y + 3 z = 0     . . . i i                 x + y + z = 0     . . . i i i                           ..... Solve the equation i   & i i i ⇒ 7 y + 6 z = 0 Solve the equation i i   & i i i ⇒ 7 x + z = 0 x = λ   &   y = - 6 - 7 λ 7   &#38