Question

The value of $x$ and $y$ respectively in the simultaneous equations $2x-\frac{3}{y}=12$ and $5x+\frac{7}{y}=1,y\ne 0$ is:

• A. $2,-\frac{2}{3}$
• B. $3,-\frac{1}{2}$
• C. $-3,-\frac{1}{2}$
• D. $-2,\frac{1}{3}$

Answer 1

The correct option is B $3,-\frac{1}{2}$

$2x-\frac{3}{y}=12$ ........ $\left(i\right)$

$5x+\frac{7}{y}=1$ ...... $\left(ii\right)$

Multiplying equation $\left(i\right)\&\left(ii\right)$ by $7$ and $3$ respectively, we have

$14x-\frac{21}{y}=84$ ...... $\left(iii\right)$

$15x+\frac{21}{y}=3$ ..... $\left(iv\right)$

Adding equations $\left(i\right)\&\left(ii\right)$, we have

$14x-\frac{21}{y}+15x+\frac{21}{y}=84+3$

$\Rightarrow 29x=87$

$\Rightarrow x=3$

Substituting the value of $x$ in $\left(i\right)$, we have

$(2\times 3)-\frac{3}{y}=12$

$\Rightarrow \frac{3}{y}=-6$

$\Rightarrow y=-\frac{1}{2}$