The length of an elastic string is x when the tension is 5N. Its length is y when the tension is 7N. What will be its length, when the tension is 9N?

We have, F=kx  where, F,x and k are force, length and constant respectively.  ∴  5=kx..........(1) and 7=ky..........(2)  Multiplying eq. (2) by 2 14=2ky..............(3)  Subtracting eq. (1) from (3).  14-5=2ky-kx or 9=k(2y-x)  Hence, required length =2y-x