Question

Solve for x and y : 15/x+y -2/x-y =1 and 15/x+y +7/x-y = 10 where x+ y not equal to 0 ,x-y not equal to 10 ​

Answer 1

Answer :

The given equations are

3/x + = … (1)

+ = … (2)

Multiplying both sides of the equation with xy,

3y + 5x = 20 i.e. 5x + 3y = 20 … (3)

2y + 5x = 15 i.e. 5x + 2y = 15 … (4)

Subtracting (4) from (3),

⇒ 5x + 3y – (5x + 2y) = 20 – 15

⇒ 5x + 3y – 5x – 2y = 5

⇒ y = 5

Substituting y = 5 in (3),

⇒ 5x + 3 (5) = 20

⇒ 5x = 20 – 15 = 5

⇒ x = 1

∴ (1, 5) is the solution for the given system.

Answer 2

Step-by-step explanation:

15/x+y - 2/x-y = 1 ------(1)

15/x+y + 7/x-y = 10 -----(2)

subtracting (1) from (2)

15/x+y + 7/x-y -[ 15/x+y -2/x-y]= 10-1

9/x-y = 9

x-y=1------(3)

Substituting x-y = 1 in equation 2,

15/x+y +7 = 10

15/x+y = 10-7=3

x+y =5------(4)

From equation 3 and 4 ,

x=3

y=2