Question

Solve the following systems of equations.
$2xy-3\frac{x}{y}=15,xy+\frac{x}{y}=15$

Answer 1

Solve the following systems of equations,

$2xy-\frac{3x}{y}=\mathrm{15...}\left(i\right)$

$xy+\frac{x}{y}=\mathrm{15....}\left(ii\right)$

To solve these equations, put $xy=a$ and $\frac{x}{y}=b$

Then, eqn (i) $\Rightarrow 2a-3b=\mathrm{15...}\left(iii\right)$

eqn (ii) $\Rightarrow a+b=15...\left(iv\right)$

Solve for a & b.

Huetiplying eqn (iv) with 2.

$\Rightarrow 2a+2b=30$

we have, $2a-3b=15(-),$ subtracting these.

_________________

$0+5b=15$

$\Rightarrow b=15/5=3$

$\therefore$ Substituting is eqn (iv), we get $a=15-3=12$

Thus, $a=xy=12$ and $b=\frac{x}{y}=3$

AS $\frac{x}{y}=3,x=3y$

Also, $xy=12\Rightarrow \left(3y\right)\times y=12$

$\Rightarrow 3y^2=12$

$\Rightarrow y^2=4$

$\Rightarrow y=\pm 2$

As, $x=3y,x=\pm 6$