Question

solve 8/x+5/y = 9 and 3/x+2/y=4

Answer 1

Answer:

The value of x is = -1/2

The value of y is = 1/5

Step-by-step explanation:

The two equations are,

8/x+5/y = 9 --------(1)

3/x+2/y = 4 ---------(2)

Now, solving these two equations,

2×(1) -5×(2),

16/x +10/y -(15/x+10/y) = (2×9) -(5×4)

=> 16/x +10/y -15/x -10/y = 18-20

=> 16/x -15/x = -2

=> (16-15) /x = -2

=> 1/x = -2

=> x = -1/2

Now putting the value of x in (1) equation, we get,

8×(-2) +5/y = 9

=> -16 +5/y = 9

=> 5/y = 9+16 = 25

=> y = 5/25 = 1/5

So, the value of x = -1/2

The value of y = 1/5

Answer 2

Answer:

the required solutions are x = 1/2 , y = -1

Step-by-step explanation:

given two equations are

8/x+5/y = 9 → (1)

3/x+2/y=4 → (2)

2 × (1) ⇒ 16/x + 10/y = 18 → (3)

5 × (2) ⇒ 15/x + 10/y = 20 → (4)

(4) - (3) ⇒

(15/x + 10/y) - (16/x + 10/y) = 20 - 18

⇒ 1/x = 2

⇒ x = 1/2

putting this value x = 1/2 in (2) we get , 3/ (1/2) + 2/y = 4

⇒ 6 + 2/y = 4

⇒ 2/y = -2

⇒ y = -1

therefore we get  x = 1/2 and y = -1 which satisfies the equation (1) and (2)

hence the solutions are x = 1/2 , y = -1