Question

The solution of set of the system of equations: $\frac{4}{x}+5y=7,\frac{3}{x}+4y=5$ is:

• A. $(\frac{1}{3},-1)$
• B. $(\frac{-1}{3},-1)$
• C. $(\frac{-1}{3},1)$
• D. $(\frac{1}{3},1)$

Answer 1

The correct option is A $(\frac{1}{3},-1)$

Let, $\frac{1}{x}=m$
The given equation
$4m+5y=7......\left(i\right)]\times 3$
$3m+4y=5.....\left(ii\right)]\times 4$
$12m+15y=21$
$12m+16y=20$
$\underset{–}{---}$
$-y=1$
$\therefore y=-1$
$4m+5(-1)=7$
$4m=12\Rightarrow m=3$
$\frac{1}{x}=m=3$
$\Rightarrow 3x=1$
$\therefore x=\frac{1}{3}$.