We know that, for infinitely many solutions,
Δ=0=Δx=Δy=Δz
So, Δ=∣α11123135∣=0
⇒α(10−9)−1(5−3)+1(3−2)=0
⇒α−2+1=0
⇒α=1
Now checking for Δx=∣54β123135∣=0
⇒5(10−9)−1(20−3β)+1(12−2β)
⇒5−20+3β+12−2β
⇒−3+β=0
⇒β=3
Hence (α,β)=(1,3)
If the system of equations αx+y+z=5,x+2y+3z=4,x+3y+5z=β. Has infinitely many solutions, then the ordered pair (α,β) is equal to
Held on 26 Jun 2022 · Verified 6 Jul 2026.
(1,−3)
(−1,3)
(1,3)
(−1,−3)
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