Answer :

Given equations are 27/(x-2) + 31/(y+3) = 85; 31/(x-2) + 27/(y+3) = 89.

Let 1/(x-2) = a and 1/(y+3) = b

Given equations becomes

27a + 31b = 85 ………………..(1)

31a + 27b = 89 ………………..(2)

Adding (1) and (2)

27a + 31b + 31a + 27b = 85 + 89

⇒ 58a + 58b = 174

⇒ 58 (a + b) = 174

⇒ a + b = 3 …………………(3)

Subtracting equation (1) and (2)

27a + 31b – 31a – 27b = 89

⇒ -4a + 4b = -4

⇒ a – b = 1 …………………(4)

Adding equation (3) and (4)

a + b + a – b = 4

⇒ 2a = 4

⇒ a = 4/2

⇒ a = 2

Putting value of a in (4)

2 – b = 1

⇒ b = 2 – 1

⇒ b = 1

Resubstituting

a = 1/(x – 2)

⇒ 1/(x – 2) = 2

⇒ 1 = 2x – 4

⇒ 2x = 1 + 4

⇒ x = 5/2

b = 1/(y + 3)

⇒ 1 = 1/(y + 3)

⇒ y + 3 = 1

⇒ y = 1 – 3

⇒ y = -2

∴ x = 5/2 and y = -2

Rate this question :

<span lang="EN-USMaharashtra Board - Algebra Papers

<span lang="EN-USMaharashtra Board - Algebra Papers

Solve the followiMHB - Mathematics Part-1

Attempt any two sMaharashtra Board - Algebra Papers

To find number ofMHB - Mathematics Part-1

Places A and B arMHB - Mathematics Part-1

The sum of fatherMHB - Mathematics Part-1

<span lang="EN-USMaharashtra Board - Geometry Papers

In a factory the MHB - Mathematics Part-1

Out of 1900 km, VMHB - Mathematics Part-1