The correct option is D p=2,q≠3
2x+py+6z=8
x+2y+qz=5
x+y+3z=4
For infinitely many solutions,
Δ=Δx=Δy=Δz=0
Δ=∣∣
∣∣2p612q113∣∣
∣∣=(p−2)(q−3)
Δx=∣∣
∣∣8p652q413∣∣
∣∣
=30−8q−15p+4pq =(p−2)(4q−15)
Δy=∣∣
∣∣28615q143∣∣
∣∣=0
Δz=∣∣
∣∣2p8125114∣∣
∣∣=p−2
At p=2, Δ=Δx=Δy=Δz=0
So, at p=2 and q∈R, the system of linear equations has infinitely many solutions.