Question

Solve the following pair of simultaneous equations:

$\frac{3}{a}+\frac{4}{b}=2;\frac{9}{a}-\frac{4}{b}=2$

• A. $a=3,b=4$
• B. $a=1,b=-2$
• C. $a=5,b=-3$
• D. $a=0,b=6$

Answer 1

The correct option is A $a=3,b=4$

$\frac{3}{a}+\frac{4}{b}=2;\frac{9}{a}-\frac{4}{b}=2$

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

So, $3x+4y=2$ and $9x-4y=2$

Adding the above equations, we get

$12x=4$

$x=\frac{1}{3}$

Substituting $x=\frac{1}{3}$ in either equation, we get $y=\frac{1}{4}$

So, $a=\frac{1}{x}=3$ and $b=\frac{1}{y}=4$

$a=3,b=4$

Option $A$.