Question

please solve the following simultaneous equations.​

Answer 1

Answer:

x = 16/17 and y = 1/17

Step-by-step explanation:

$\sqrt{\dfrac{x}{y} } = 4 \text { ---------------- [ 1 ]}$

$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{xy} \text { ---------------- [ 2 ]}$

From [ 1 ]:

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

$\dfrac{x}{y} = 16$

$x = 16y \text{ --------------- [ 3 ]}$

From[2}:

$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{xy}$

$\dfrac{y + x}{xy} = \dfrac{1}{xy}$

$y + x = 1 \text{ ------------- [ 4 ] }$

Sub [ 3 ] into [ 4 ]:

$y + x = 1$

$y + 16y = 1$

$17y = 1$

$y = \dfrac{1}{17}$

Sub value of y into [ 4 ] :

$y + x = 1$

$\dfrac{1}{17} + x = 1$

$x = 1 - \dfrac{1}{17}$

$x = \dfrac{16}{17}$

Answer: x = 16/17 and y = 1/17