Question

If $\frac{2}{x}+\frac{3}{y}=\frac{9}{xy}and\frac{4}{x}+\frac{9}{y}=\frac{21}{xy}$,find the values of x and y.

Answer 1

The given system of equation is

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

$\to \frac{2y+3x}{xy}=\frac{9}{xy}$​​​​​​​

$3x+2y=9$ ....(1)

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

$\to \frac{4y+9x}{xy}=\frac{21}{xy}$​​​​​​​

$\to 9x+4y=21$......(2)

multiplying (1) by 2 and subtracting it from (2), we get

3x=3

x=1

putting value of x in any of the equations we get

y=3

Thus, the solution of the given equations is x = 1 and y = 3.