If 2 cos theta + sin theta = 1 , then 7 cos theta + 6 sin theta =

(1) 1 or 6

(2) 2 or 3

(3) 2 or 4

(4) 2 or 6

Multiply 6 in first equation i.e 2costheta+sintheta=1 .
We get 12costheta +6sintheta=6
Now let, 7costheta+6sintheta=K
Eliminate sintheta , and get values of sintheta and costheta in terms of K
Sintheta=2K-7/5 , costheta=6-K/5
NOW we know sinsqauretheta +cossquaretheta=1 .put values here in terms of K and then a quadratic equation in K will form , on solving it we get K=6 or 2.hence proov