Linear Equation 23

Solve : 30 / (x - y) + 44 / (x + y) = 10 and 40 / (x - y) + 55 / (x + y) = 13

Solution:

Let 30 / (x - y) + 44 / (x + y) = 10 --------------------------------------- (i)

40 / (x - y) + 55 / (x + y) = 13 ------------------------------------------- (ii)

Multiplying equation (i) by 4 and equation (ii) by 3, we get

120 / (x - y) + 176 / (x + y) = 40 ---------------------------------------- (iii)

120 / (x - y) + 165 / (x + y) = 39 ---------------------------------------- (iv)

Subtracting (iv) from (iii) , we get

11 / (x + y) = 1 ; => x + y = 11 ----------------------------------------- (v)

Now, 30 / (x - y) + 44 / (x + y) = 10

=> 30 / (x - y) + 44 / 11 = 10

=> 30 / (x - y) = 6

=> 6 (x - y) = 30 and (x - y) = 5 ---------------------------------------- (vi)

On solving equations (v) and (vi), we get : x = 8 and y = 3

Therefore, Solution is : x = 8 and y = 3

Alternative method :

Let x - y = a and x + y = b

Therefore, 30 / (x - y) + 44 / (x + y) = 10

=> 30 / a + 44 / b = 10 ------------------------------------------------- (i)

and, 40 / (x - y) + 55 / (x + y) = 13

=> 40 / a + 55 / b = 13 ------------------------------------------------ (ii)

Multiplying equation (i) by 4 and equation (ii) by 3, we get

120 / a + 176 / b = 40 ------------------------------------------------- (iii)

120 / a + 165 / b = 39 ------------------------------------------------- (iv)

Subtracting (iv) from (iii) , we get

11 / b = 1

=> b = 11 and x + y = 11 ---------------------------------------------- (v)

30 / a + 44 / b = 10

=> 30 / a + 44 / 11 = 10

=> 30 / a = 10 - 4

=> a = 5 and x - y = 5 ----------------------------------------------- (vi)

On solving equations (v) and (vi) , we get

x = 8 and y = 3