Question

Find the value (s) of for which the system of equations below has infinitely many solutions. ( a-3)x+y=0 x+( a-3 ) y=0

Answer 1

Two equation ax+by=0 and cx+dy=0 has infinitely many solution only if a/c=b/d=some constant.

For this given problem after simplifying, from (1) & (2) we see that both has x coefficient 1 and so ratio of y coefficient of (1) & (2) must be 1 , so they are equal. Using this concept i found the values of a for this given problem.