Question

If $4x+6y=3xy\mathrm{and}8x+9y=5xy$ then
(a) x = 2, y = 3 (b) x = 1, y = 2 (c) x = 3, y = 4 (d) x = 1, y = − 1

Answer 1

The given equations are
$$\begin{gathered} 4x+6y=3xy.....\left(i\right) \\ 8x+9y=5xy.....\left(ii\right) \end{gathered}$$
Dividing (i) and (ii) by xy, we get
$$\begin{gathered} \frac{6}{x}+\frac{4}{y}=3.....\left(iii\right) \\ \frac{9}{x}+\frac{8}{y}=5.....\left(iv\right) \end{gathered}$$
Multiplying (iii) by 2 and subtracting (iv) from it, we get
$\frac{12}{x}-\frac{9}{x}=6-5\Rightarrow \frac{3}{x}=1\Rightarrow x=3$
Substituting x = 3 in (iii), we get
$\frac{6}{3}+\frac{4}{y}=3\Rightarrow \frac{4}{y}=1\Rightarrow y=4$
Thus, x = 3 and y = 4.
Hence, the correct answer is option (c).