Question

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{7x-2y}{xy}=5,\frac{8x+7y}{xy}=15$

• A. $x=0,y=2$
• B. $x=2,y=7$
• C. $x=13,y=0$
• D. $x=1,y=1$

Answer 1

Answer: (D)

$x=1,y=1$

The given equations are $\frac{7x-2y}{xy}=5\&\frac{8x+7y}{xy}=15.$

On simplifying, we get

$\frac{7}{y}-\frac{2}{x}=5$ and $\frac{8}{y}+\frac{7}{x}=15$

Let $\frac{1}{x}=u$ and $\frac{1}{y}$

Then the equations reduce to

$7v-2u=5$ ...(i) and

$8v+7u=15$ ...(ii)

Multiplying (i) by $8$ and (ii) by $7$, we get

$56v-16u=40$ ...(iii) and

$56v+49u=105$ ...(iv)

Subtracting (iv) from (iii),

$-65u=-65$ $\Rightarrow u=1$.

$\therefore \frac{1}{x}=1\Rightarrow x=1$

Putting $u=1$ in $\left(i\right)$,

$7v-2\times 1=5\Rightarrow v=1\Rightarrow \frac{1}{y}=1\Rightarrow y=1$

So $(x,y)=(1,1)$