The fastest way I can come up with is this, and hopefully is the right process.
To prove :- s=3r+2

(1) equation of the form ab=0
implies a=0 or b=0, cannot proceed
(2) equation of the form ac=0
implies a=0 or c=0.

Combining, and understanding that there is no way b=c(look closely at the equations)
we get a=0, which means
s=3r+2
Hence proved.

The fastest way I can come up with is this, and hopefully is the right process.
To prove :- s=3r+2

(1) equation of the form ab=0
implies a=0 or b=0, cannot proceed
(2) equation of the form ac=0
implies a=0 or c=0.

Combining, and understanding that there is no way b=c(look closely at the equations)
we get a=0, which means
s=3r+2
Hence proved.

my way is this:

first is insuf and the second. since we can not decide which one is zero.
but:
the first part of statement1 and the second part of the statement2 is equal and the second part of the statement 1 and firs part of the statement 2 have the difference of 15 and with the same coefficient for r and s. so the first part of statement1 and the second part of the statement2 is equal to zero, which means Yes to answer and choice C.