Find the value of k for which each of the following systems of equations has no solution:
kx+3y=3,12x+ky=6.
Equations are written as
kx + 3y – 3 = 0 .....(1)
12x + ky – 6 = 0 ....... (2)
a1=k, b1=3, c1=−3
a2=12, b2=k, c2=−6
for no solution we must have:
a1a2=b1b2≠c1c2Now,
k12=3k≠−3−6Hence, k = -6
Hence, the given system of equations is has no solution if k =-6.