Question

Solve each pair of equation by using the substitution method.
$x+\frac{6}{y}=6$
$3x-\frac{8}{y}=5$

• A. $x=3$ and $y=-2$
• B. $x=30$ and $y=2$
• C. $x=3$ and $y=2$
• D. None of these

Answer 1

Answer: (C)

$x=3$ and $y=2$

$x+\frac{6}{y}=\mathrm{6......}\left(i\right)$

$3x-\frac{8}{y}=\mathrm{5.....}\left(ii\right)$

From equation $\left(i\right)$, we get

$\Rightarrow x=6-\frac{6}{y}...\left(iii\right)$

Substituting value of $x$ in equation $\left(ii\right)$, we get

$3(6-\frac{6}{y})-\frac{8}{y}=5$

$\Rightarrow 18-\frac{18}{y}-\frac{8}{y}=5$

$\Rightarrow \frac{-26}{y}=-13$

$\Rightarrow y=2$

Substituting the value of $y$ in (iii)

$x=6-\frac{6}{2}=3$

$\therefore x=3,y=2$