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# Solve the following systems of equations: 1/(3x + y) + 1/(3x - y) = 3/4 1/(2(3x + y)) - 1/(2(3x - y)) = -1/8 - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Substitution Method

#### Question

Solve the following systems of equations:

1/(3x + y) + 1/(3x - y) = 3/4

1/(2(3x + y)) - 1/(2(3x - y)) = -1/8

#### Solution

The given equation is

1/(3x + y) + 1/(3x - y) = 3/4

1/(2(3x + y)) - 1/(2(3x - y)) = -1/8

Let 1/(3x + y) = u and 1/(3x - y) = v then equation are

u + v = 3/4 ...(i)

u/2 - v/2 = 1/8 ....(ii)

Multiply equation (ii) by 2 and add both equations, we get

u + v = 3/4

u - v = -1/4

2u = 1/2

u = 1/4

Put the value of u  in equation (i) we get

1 xx 1/4 + v = 3/4

v= 1/2

Then

1/(3x + y) = 1/4   ....(iii)

3x  + y = 4

1/(3x -y) = 1/2  ...(iv)

3x - y = 2

3x + y = 4

3x - y = 2

_________

6x = 6

x = 1

Put the value of x in equation (iii) we get

3 x 1 + y = 4

y = 1

Hence value of x = 1 and  y = 1

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Solution Solve the following systems of equations: 1/(3x + y) + 1/(3x - y) = 3/4 1/(2(3x + y)) - 1/(2(3x - y)) = -1/8 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method.
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