# Solve the Following Systems of Equations: 3/(X + Y) + 2/(X - Y) = 2 9/(X + Y) - 4/(X - Y) = 1 - Mathematics

Solve the following systems of equations:

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

9/(x + y) - 4/(x - y) = 1

#### Solution

Let 1/(x + y) = u and 1/(x - y) = v  Then, the given system of equation becomes

3u + 2v = 2 ....(i)

9u + 4v = 1 ...(ii)

Multiplying equation (i) by 3, and equation (ii) by 1, we get

6u + 4v = 4  ....(iii)

9u - 4v = 1 ...(iv)

Adding equation (iii) and equation (iv), we get

6u + 9u = 4 +1

=> 15u = 5

=> u = 5/15 = 1/3

Putting u = 1/3 in equation (i) we get

3 xx 1/3 + 2v = 2

=> 1 + 2v = 2

=> 2v = 2 - 1

=> v = 1/2

Now, u = 1/(x + y)

=> 1/(x + y) = 1/3

=> x + y = 3  ....(v)

And v = 1/(x - y)

=> 1/(x - y) = 1/2

=> x - y = 2 .....(vi)

Adding equation (v) and equation (vi), we get

2x = 3 + 2

=> x = 5/2

Putting x = 5/2 in equation (v) we get

5/2 + y  = 3

=> y = 3 - 5/2

=> y = (6-5)/2 = 1/2

Hence, solution of the given system of equation is  x = 5/2, y = 1/2

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 31 | Page 45