Question

Solve for X and Y:2/x+3/y=9/xy;4/x+9/y=21/xy (x=0.y=0)​

Answer 1

$\mathfrak{\huge{Answer:}}$

The Given equations are :

$\tt{\frac{2}{x} + \frac{3}{y} = \frac{9}{xy}\:and\:\frac{4}{x} + \frac{9}{y} = \frac{21}{xy}}$

In these types of questions, generally, we assume the values of $\sf{\frac{1}{x}\:and\:\frac{1}{y}}$ to be m and n respectively, or even any other variable. But since here, we're even given the term 'xy' on the R.H.S., we can solve it by simply taking LCM. This would lessen up our calculations. Proceed further :

Take the LCM :

$\tt{\frac{2y + 3x}{\cancel xy} = \frac{9}{\cancel xy}}$

=》 2y + 3x = 9

The other equation :

$\tt{\frac{4y + 9x}{\cancel xy} = \frac{21}{\cancel xy}}$

=》 4y + 9x = 21

=》 4y + 9x - 21 = 0

I'll use the elimination method for solving the question further. You can use any other method too.

Make the coefficients of y the same :

=》 2 ( 2y + 3x ) = 2 ( 9 )

=》 4y + 6x = 18

=》 4y + 6x - 18 = 0

Now subtract both the equations to get the values of x and y :

=》 4y + 6x - 18 - ( 4y + 9x - 21 ) = 0

=》 4y + 6x - 18 - 4y - 9x + 21 = 0

=》 ( -3x ) = ( -3 )

=》 x = 1

y = $\sf{\frac{9 - 3}{2}}$

y = 3