Let a, b and c be three real numbers satisfyinga    b    c1    9    78    2    77    3    7=0    0    0                        (1)If the point P(a,b,c) with reference to (1), lies on the plane 2x + y + z = 1, then the value of 7a+b+c is

We have a+8b+7c=0, 9a+2b+3c=0, 7a+7b+7c=0Subtracting the last equation from first and multiplying thelast equation by (9/7) and subtracting from the second equationwe obtain −6a+b=0,7b+6c=0⇒ a1=b6=c−7=k (say)Thus, a=k,b=6k,c=−7k.As (a,b,c)=(k,6k,−7k) lies on 2x+y+z=1, we get k=1.Thus,  7a+b+c=7k+6k−7k=6k=6