In (2x+3y=21) and (x+y=8), what will be the value of (y)?

Correct answer: (y=5)

Use the simpler equation \\(x+y=8\\) to isolate x: \\(x=8-y\\). Substitute this into \\(2x+3y=21\\): \\(2(8-y)+3y=21\\). Expanding gives \\(16-2y+3y=21\\), so \\(16+y=21\\). Therefore \\(y=5\\), which is option C. The substitution is valid because the first equation directly supplies x in terms of y.

Now verify x: from \\(x=8-y\\), x equals \\(8-5=3\\). Substituting \\(x=3,y=5\\) into the first equation gives \\(2(3)+3(5)=6+15=21\\), and the second gives \\(3+5=8\\). Both equations hold, so no alternative listed value works. Thus the supplied answer C is correct.