Question

Solve the following pair of simultaneous equations:

$\frac{8}{x}-\frac{9}{y}=1;\frac{10}{x}+\frac{6}{y}=7$

• A. $x=2;y=3$
• B. $x=7;y=5$
• C. $x=4;y=6$
• D. $x=1;y=7$

Answer 1

The correct option is A $x=2;y=3$

Let $\frac{1}{x}=a$ and $\frac{1}{y}=b$

We have, $8a-9b=1$ ...$\left(1\right)$

$10a+6b=7$ ...$\left(2\right)$

Multiplying $\left(1\right)$ by $10$ and $\left(2\right)$ by $8$

We get,

$80a-90b=10$

$80a+48b=56$

Subtracting, we get $-138b=-46$

$\therefore b=\frac{1}{3}$.

Substituting in $\left(1\right)$ or $\left(2\right)$, we get $a=\frac{1}{2}$

So, $x=2$ and $y=3$.

Option $A$