Question

Solve each of the following systems of equations by the method of cross-multiplication:
2/x + 3/y =135/x - 4/y =-2 where x ≠ 0, y ≠ 0

Answer 1

Therefore the solution is

$x = -\frac{59}{2}$   and   $y=-\frac{59}{38}$

Step-by-step explanation:

Given equation are

$\frac{2}{x}+\frac{3}{y}=-2$.....(1)

and

$\frac{135}{x}-\frac{4}{y}=-2$......(2)

To solve the equations let $\frac{1}{x}=u$  and  $\frac{1}{y}=v$

The equation becomes

$2u+3v+2=0$

and $135u-4v+2=0$

Now solving this equation by the method of cross multiplication

$\frac{u}{3.2-2.(-4)}=\frac{v}{135.2-2.2}=\frac{1}{2.(-4)-3.135}$

$\Rightarrow \frac{u}{14}=\frac{v}{266}=\frac{1}{-413}$

Therefore,

$u=-\frac{14}{413}$      and   $v=-\frac{266}{413}$

Putting  $\frac{1}{x}=u$  and  $\frac{1}{y}=v$

$\frac{1}{x}=-\frac{14}{413}$       and   $\frac{1}{y}=-\frac{266}{413}$

$\Rightarrow x =-\frac{413}{14}$            $y=- \frac{413}{266}$

$\Rightarrow x = -\frac{59}{2}$              $y=-\frac{59}{38}$

Therefore the solution is

$x = -\frac{59}{2}$   and   $y=-\frac{59}{38}$