Question

Does the linear system

ax + by = 0
cx + dy = 0

always have a solution for any value of a,b,c and d ?

Answer 1

hint:
if the quantity:
\[\Delta= ad - bc \ne 0\]
then the system has one solution only, since the Matrix of the coefficients of the system is not singular
so, please you have to investigate the case: \(\Delta=0\)

Answer 2

x=y=0