Question

Solving $\frac{5}{2+x}+\frac{1}{y-4}=2$; $\frac{6}{2+x}-\frac{3}{y-4}=1,wegetx=y=$

• A.
  1 and 7
• B.
  2 and 7
• C.
  3 and 4
• D.
  4 and 1

Answer 1

The correct option is A

1 and 7
Let, $p=dfrac12+xandq=\frac{1}{y-4}\text{Thus, given equations reduce to,}5p+q=\mathrm{2...}\left(i\right)6p-3q=\mathrm{1...}\left(ii\right)\text{On multiplying (i) by 3 and then adding it to (ii), we get}15p+3q=66p-3q=12p=7\Rightarrow P=\frac{1}{3}\text{and on substituting this value in (ii) we get}6\times \frac{1}{3}-3q=1\Rightarrow q=\frac{1}{3}Now,P=\frac{1}{2+x}\Rightarrow x=1\text{we know that}q=\frac{1}{y=4}\Rightarrow \frac{1}{x}=\frac{1}{y-4}\Rightarrow y=7$