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Solve the following pairs of equations by reducing them to a pair of linear equations: (viii) 1/(3x+y) + 1/(3x-y) = 3/4 1/2(3x+y) – 1/2(3x-y) = -1/8 Q.1(8)

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What is the  best way for solving this question, I don’t know how to solve this question because it is very tough for me so please suggest me some solution Solve the following pairs of equations by reducing them to a pair of linear equations: (viii) 1/(3x+y) + 1/(3x-y) = 3/4 1/2(3x+y) – 1/2(3x-y) = -1/8

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1. Substituting 1/(3x+y) = m and 1/(3x-y) = n in the given equations, we get,

m + n = 3/4 …………………………….…… (1)

m/2 – n/2 = -1/8

m – n = -1/4 …………………………..…(2)

Adding (1) and (2), we get

2m = 3/4 – 1/4

2m = 1/2

Putting in (2), we get

1/4 – n = -1/4

n = 1/4 + 1/4 = 1/2

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

3x + y = 4 …………………………………(3)

n = 1/( 3x-y) = 1/2

3x – y = 2 ………………………………(4)

Adding equations (3) and (4), we get

6x = 6

x = 1 ……………………………….(5)

Putting in (3), we get

3(1) + y = 4

y = 1

Hence, x = 1 and y = 1

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