Question

Find the value of x and y.​

Answer 1

Solution

Given :-

• 10/(x+y) + 2/(x-y) = 4 ---------(1)
• 15/(x+y) - 9/(x-y) = -2 ---------(2)

Find :-

• Value of x & y

Explanation

Let,

• 1/(x+y) = p
• 1/(x-y) = q

So, New equation will be

• 10p + 2q = 4 -------------(3)
• 15p - 9q = -2 -------------(4)

Multiply by 9 in equ(3) & 2 in equ(4)

• 90p + 18q = 36
• 30p - 18q = -4

_______________ Add it's

==> 90p + 30p = 36 - 4

==> 120p = 32

==> p = 32/120

==>p = 4/15

Keep Value in equ(3)

==> 10 * 4/15 + 2q = 4

==> 2q = 4 - 40/15

==>2q = (4*15-40)/15

==>2q = (60-40)/15

==>2q = 20/15

==> q = 20/(15*2)

==> q = 10/15

==>q = 2/3

____________________

Hence

• Value of p = 4/15
• Value of q = 2/3

________________

So,

==> 1/(x+y) = 4/15

==> x + y = 15/4 ----------(5)

And,

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

==> x - y = 3/2 ---------(6)

Add equ(5) & equ(6)

==> 2x = 15/4 + 3/2

==>2x = (15 + 3*2)/4

==> 2x = (15+6)/4

==> 2x = 21/4

==>x = 21/8

Keep Value of x in equ(5)

==> 21/8 + y = 15/4

==>y = 15/4 - 21/8

==> y = (15*2 - 21)/8

==> y = (30-21)/8

==> y = 9/8

___________________

Since

• Value of x = 21/8
• Value of y = 9/8

________________

Answer Verification

Keep Value of x & y in equ(5)

==> 21/8 + 9/8 = 15/4

==> (21+9)/8 = 15/4

==> 30/8 = 15/4

==> 15/4 = 15/4

L.H.S. = R.H.S.

Thats proved.

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