Question

Convert the following equations into simultaneous equations and
solve :
√x/√y =4 ; 1/x + 1/y = 1/ xy​

Answer 1

Solving Equations

$\frac{\sqrt{x} }{\sqrt{y} } = 4$

Squaring both sides :-

$\frac{x}{y} = 16\\\\x = 16 y\ ...........................................................Eq(1)$

Now, simplify the second equation :-

$\frac{1}{x} +\frac{1}{y} = \frac{1}{xy} \\\\\frac{x + y}{xy} = \frac{1}{xy} \\\\x + y=1 ............................................Eq.(2)$

Now, substitute the value of x from Eq.(1) in Eq.(2).

$16y + y = 1\\\\17y = 1\\\\\boxed{ \: y= \dfrac{1}{17} }}$

Now, substitute the value of y in Eq.(1) to get the value of x.

$x = 16y\\\\x = 16 *\frac{1}{17} \\\\\\\boxed{ x = \frac{16}{17} }}$