Question

If $\frac{4}{x}+5y=7$ and $\frac{3}{x}+4y=5$, then find the value of x and y.

• A. $x=\frac{1}{3},y=1$
• B. $x=\frac{-1}{3},y=-1$
• C. $x=\frac{1}{3},y=-1$
• D. $x=-\frac{1}{3},y=1$

Answer 1

The correct option is C $x=\frac{1}{3},y=-1$

Given that,
$\frac{4}{x}+5y=7\frac{3}{x}+4y=5$
Let $\frac{1}{x}$ = t
$4t+5y=7$....................(1)
& $3t+4y=5$................(2)
Multiplying eq. (1) by $3$ & eq. (2) by $4$, we get
$12t+15y=21$
$12t+16y=20$
$-y=1$
$y=-1$
Putting $y=-1$ in equation (I). we get
$t=3$
then,$\frac{1}{x}$ = t = $3$ or x = $\frac{1}{3}$