Question

solve( 16/x+y )+( 2/ x-y) = 11;( 8/x + y) - (12 /x-y) = 7​

Answer 1

(16/x+y) + (2/ x-y) = 11 (8/x + y) - (12 /x-y) = 7

• 1/x+y = a. & 1/x-y = b

16a + 2b = 11 _(i) 8a - 12b = 7 _(ii)

• Divide (i) by 2

8a + b = 11/2 _(iii) 8a - 12b = 7 _(iv)

• (iii) - (iv)

8a - 12b - (8a + b) = 7 - 11/2

8a - 12b - 8a - b = 3/2

-12b = 3/2

b = -1/8

• Put b = -1/8 in eqn (iv)

8a - 12*-1/8 = 7

8a + 3/2 = 7

16a + 3 = 14

16a = 11

a = 11/16

NOW

• 1/x-y = -1/8
• -(x-y) = 8
• y - x = 8
• 11y - 11x = 88 _(1)

• 1/x+y = 11/16
• 11x + 11y = 16 (2)

Add (1) & (2)

• 22y = 104
• y = 104/22 = 52/11
• x = 52/11 - 8 = -36/11