1ax+by=0 and cx+dy=0
we have to choose a,b,c,d from {0,1}
for a,b,c,d total number of options are 24. the equation has unique solution then
a/c≠b/d
if ad≠bc
ad=0
and bc=1
ad=0 where (a,d) is (0,0),(1,0),(0,1) and bc=1 if (b,c) is (1,10
total cases of ad=0 and bc=1 is3
similarly ad=1 and bc=0 gives 3 solutions then the total number of solutions for ad≠bc is 6
then probability that the system of equations has unique solutions =6/16=3/8
this system of equation has always a solution then the probability is 1
hence option B