Question

xy/x+y = 5/6second equation xy/x-y = 6 solve the equation in elimination method

​

Answer 1

PLEASE, PLEASE,PLEASE, PLEASE, PLEASE,

MARK IT AS A BRAINLIEST ANSWER

THESE ANSWER IS WRITTEN BY ME

Answer 2

AnswEr

The value of

x = 60/31

y = 60/41

Given

The equations are :

• $\sf{ \frac{xy}{x + y} = \frac{5}{6} }$
• $\sf{ \frac{xy}{x - y} = 6}$

To Find

• The value of x and y

Solution

$\sf{ \frac{xy}{x + y} = \frac{5}{6} }$

$\sf{\implies \frac{x + y}{xy} = \frac{6}{5} }$

$\sf{ \implies\frac{1}{y} + \frac{1}{x} = \frac{6}{5} - - - (1) }$

And the other one

$\sf{ \frac{xy}{x - y} = 6}$

$\sf{ \implies\frac{x - y}{xy} = \frac{1}{6}}$

$\sf{ \implies \frac{1}{y} - \frac{1}{x} = \frac{1}{6} - - - (2)}$

Let us consider 1/x = p and 1/y = q so that the equations (1) and (2) becomes

$\sf{q + p = \frac{6}{5} - - - (3) }$

and

$\sf{ \implies q - p = \frac{1}{6} - - - (4)}$

Adding equation (3) and (4) we have

$\sf{q + p + q- p= \frac{6}{5} + \frac{1}{6} }$

$\sf{\implies 2q= \frac{5 + 36}{30} }$

$\sf{\implies q= \frac{41}{30 \times 2} }$

$\sf{ \implies q= \frac{41}{60} }$

And Using the value of q in (4)

$\sf{ \implies \frac{41}{60} - p = \frac{1}{6} }$

$\sf{ \implies - p= \frac{1}{6} - \frac{41}{60} }$

$\sf{ \implies p= \frac{31}{60} }$

Since p = 1/x

$\sf{\implies \frac{1}{x} = \frac{31}{60} }$

$\boxed{\sf{ \implies x = \frac{60}{31} }}$

And q = 1/y

$\sf{ \implies \frac{1}{y} = \frac{41}{60} }$

$\boxed{ \sf{ \implies y = \frac{60}{41} }}$