Question

HOTS Question:
Solve: 2xy /x+y = 3/2, x+y≠0 and xy / 2x-y = -3 / 10, 2x-y≠0

Answer 1

$x = \frac{1}{2}$ and $y = - \frac{3}{2}$

Step-by-step explanation:

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

$= > \frac{x + y}{xy} = \frac{4}{3}$

$= > \frac{1}{x} + \frac{1}{y} = \frac{4}{3}$---- Eq. 1

Then,

$\frac{xy}{2x - y} = - \frac{3}{10}$

$= > \frac{2x - y}{xy} = - \frac{10}{3}$

$= > - \frac{1}{x} + \frac{2}{y} = - \frac{10}{3}$-- Eq. 2

Let

$\frac{1}{x} = u$and

$\frac{1}{y} = v$.

Then, from Eq. 1 & 2, we get:

$u + v = \frac{4}{3}$ and

$- u + 2v = - \frac{10}{3}$

$= > 3u + 3v = 4$and

$- 3u + 6v= - 10$

By adding, we get,

$9v = - 6$

$= > v = \frac{ - 6}{9}$

$= > v = - \frac{2}{3}$

Substituting "y" got above in Eq.1, we get,

$\frac{1}{x} - \frac{2}{3} = \frac{4}{3}$

$= > \frac{1}{x} = \frac{6}{3} = 2$

$= > x = 2$

Hence,

$x = \frac{1}{2}$

$= > y = - \frac{3}{2}$

Answer 2

The value of x in the given expression is ²/₃ and y is -6.

Simplification of the linear equation

The given linear equation can be simplified by equating the variables to the equivalent values as shown below;

$\frac{2xy}{x + y} = \frac{3}{2} \\\\4xy = 3x + 3y\ \ ---(1)$

Equation (2) is obtained as follows;

$\frac{xy}{2x - y} = \frac{-3}{10} \\\\10xy = -6x + 3y \ ---(2)$

Multiple equation (1) by 2

8xy = 6x + 6y

Add equation (1) and (2) together

8xy = 6x + 6y

10xy = -6x + 6y

---------------------------

18xy = 12y

divide both sides by "y"

18x = 12

x = 12/18

x = ²/₃

Solve for y

8y x (²/₃) = 6(²/₃) + 6y

16y/3 = 12/3 + 6y

Multiply through by 3

16y = 12 + 18y

-2y = 12

y = -6

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