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2xy/x + y = 3/2. xy/2x - y = -3/10. x + y ≠ 0, 2x - y ≠ 0, solve the equation

Solution:

From the above question, we have the equation as,

2xy/x + y = 3/2---------------(1)

xy/2x - y = -3/10-------------(2)

Rearranging the above equations,

x/xy + y/xy = 4/3

2/y - 1/x = -10/3.

Consider

u = 1/x

v = 1/y

Again rearranging the equations, we get,

v + u = 4/3--------------------------(3)

2v - u = -10/3----------------------(4)

For solving these equations, add both the equations. We get,

3v = 4/3 - 10/3 = -6/3

3v = -2

v = -2/3.

Substitute the value of v in(3),we get,

-2/3 + u = 4/3

u = 2.

x = 1/u = 1/2

y = 1/v = -3/2.

x = 1/2

y = -3/2.

Therefore the required values of x and y are 1/2 and -3/2 respectively.

✦ Try This: Solve the following equation: 2xy/x + y = 5/2. xy/2x - y = -7/10. x + y ≠ 0, 2x - y ≠ 0

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 9 (vii)

Summary:

Solving the following equation 2xy/x + y = 3/2, xy/2x - y = -3/10, we get the required values of x and y as 1/2 and -3/2 respectively.

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