1/3x + y + 1/3x - y = 3/4 , 1/2(3x + y) - 1/2(x-y) = -1/8 - Solve the Pair of Equations by Reducing them to a Pair of Liner Equations | Bzziii.com

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Solve the pair of equations by reducing them to a pair of liner equations.

`\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}`

`\frac{1}{2(3x+y)}+\frac{1}{2(3x-y)}=\frac{-1}{ 8}`







`\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}`

Let a= `1/3` x + y   , and b= `1/"3x"` - y

a + b = 3/4       ....... (i)

4a + 4b = 3      ....... (ii)

also ,

`\frac{1}{2(3x+y)}+\frac{1}{2(3x-y)}=\frac{-1}{ 8}`

`"a"/2` - `"b"/2` = `"-1"/"8"`

`"(a - b)"/"2"` = `"-1"/"8"`

a - b = `"-1"/"4"`

4a - 4b = -1      ....... (ii)

Adding equations (i) and (ii) 

4a + 4b = 3

4a - 4b = -1

8a = 2

a = `2/8`

a = `1/4`

4a - 4b = -1

4 `\times` `1/4` - 4b = -1

1 - 4b = -1

4b = 1 + 1

4b = 2

b = `2/4`

b = `1/2`

`"1"/"3x"` + y = a

`"1"/"3x"` + y = `1/4`

3x + y = 4       ....... (iii)

1/3x - y = b

1/3x - y = 1/2

3x - y = 2       ....... (iv)
Adding equations (iii) and (iv) :-

3x + y = 4
3x - y = 2



6x = 6

x = 1

3x + y = 4
3 `\times` 1 + y = 4

y = 4 - 3 = 1

Hence,

x = 1 , y = 1

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