For all real values of a and b 2a+bx+a+3by+b−3a=0 and mx+2y+6=0 are concurrent, then m is equal to

The given family of lines can be rewrite as   a2x+y−3+bx+3y+1=0All these lines  are passing through the point of intersection of   2x+y−3=0,x+3y+1=0Hence, the point of intersection of those two lines is   2,−1Since the line  is mx+2y+6=0 concurrent with the given family of lines, the line  mx+2y+6=0 passes through the fixed point   2,−1It implies that   2m−2+6=0⇒m=−2