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Consider the family of lines 5x+3y-2+lam...

Consider the family of lines `5x+3y-2+lambda_(1)(3x-y-4)=0 " and " x-y+1+lambda_(2)(2x-y-2)=0`. Find the equation of a straight line that belongs to both the families.

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The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

If it is possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) a=-2 (d) a=2