If for some  αand βin R, the intersection of the following three planesx+4y-2z=1x+7y-5z=βx+5y+α z=5 is a line in R3, then α+β is equal to:

Given 3 planes has line of intersection which means infinite solutions So, Δ=0⇒14-217-515α=0⇒(7α+25)-(4α+10)+(-20+14)=0⇒α=-3 Also Dz=0⇒14117β155=0⇒1(35-5β)-(15)+1(4β-7)=0⇒β=13α+β=-3+13=10