Question

Solve the equation using elimination method:
$\frac{3}{x}+\frac{2}{y}=7$ and $\frac{4}{x}-\frac{1}{y}=2$

• A. $(1,\frac{1}{2})$
• B. $(-1,\frac{1}{2})$
• C. $(1,\frac{-1}{2})$
• D. $(-1,\frac{-1}{2})$

Answer 1

Answer: (A)

$(1,\frac{1}{2})$

Let us assume $\frac{1}{x}=u;\frac{1}{y}=v$, then the equation becomes,

$3u+2v=7$ .....(1)

$4y-v=2$ .....(2)

Multiply the equation (2) by $2$ and then subtract the equation

$3u+2v=7$

$8u-2v=4$

__________

$11u=11$

$\Rightarrow u=\frac{11}{11}=1$

$\Rightarrow u=\frac{1}{x};x=1$

Put the value of $u$ in equation (2), we get

$4u-v=2$

$\Rightarrow 4\left(1\right)-v=2$

$\Rightarrow 4-2=v$

$\Rightarrow v=2$

Therefore, the solution is $(1,\frac{1}{2})$.