Question

Solve the following simultaneous equations.

`10/("x" + "y") + 2/("x" - "y") = 4; 15/("x" + "y") - 5/("x" - "y") = -2`

Answer 1

`10/("x" + "y") + 2/("x" - "y") = 4; 15/("x" + "y") - 5/("x" - "y") = -2`

Let `1/("x" + "y")` = u and `1/("x" - "y")` = v

So, the equation becomes

10u + 2v = 4 ....(I)

15u − 5v = −2 ....(II)

Multiplying (I) with 5 and (II) with 2 we get

50u + 10v = 20 ....(III)

30u − 10v = −4 .....(IV)

Adding (III) and (IV) we get

u = `16/80 = 1/5`

Putting this value in (I)

`10 xx 1/5 + 2"v" = 4`

⇒ 2 + 2v = 4

⇒ 2v = 4 - 2

⇒ 2v = 2

⇒ v = `2/2`

⇒ v =  1

`1/("x" + "y") = 1/5` and `1/("x" - "y")` = 1

⇒ x + y = 5 and x − y = 1

Solving these equations we get

x + y = 5
x − y = 1
2x = 6

x = `6/2`

x = 3

put x = 3 in the equation (x − y = 1)

3 − y = 1

3 − 1 = y

y = 2