If $4 x+3 y=18 x y$ and $2 x-5 y+4 x y=0$, then the values of $x$ and $y$ will be respectively
(a)$-\frac{1}{2}$ and $-\frac{1}{3}$
(b)- 1 and - 3
(c)$\frac{1}{2}$ and $\frac{1}{3}$
(d)$\frac{1}{4}$ and $\frac{1}{3}$
Answer
Answer (as printed): C
Explanation
$4 x+3 y=18 x y \quad \ldots(i)$ and $2 x-5 y=-4 x y \quad \ldots(i i)$ Dividing (i) and (ii) by $x y$, we get: $$\frac{3}{x}+\frac{4}{y}=18 \quad \ldots(i i i) \text { and } \frac{5}{x}-\frac{2}{y}=4$$ Multiplying (iv) by 2 and adding (iii) to it, we get: $$\frac{13}{x}=26 \text { or } x=\frac{1}{2} \text {. }$$ Putting $x=\frac{1}{2}$ in (iii), we get : $y=\frac{1}{3}$.
Explanation as extracted from the printed page; notation may be imperfect.