If $$2x-3y=7$$​ and $$\frac{x}{x+y}=\frac{5}{6}$$​, then what is the value of $$x-y$$​?

Correct option is A

Given:

​$$2x - 3y = 7 \quad \text{(i)} \\ \dfrac{x}{x + y} = \dfrac{5}{6} \quad \text{(ii)}$$​​

We are to find the value of x - y.

Solution:

From equation (ii):

6x = 5(x + y)

6x = 5x + 5y

x = 5y ….(iii)

Substitute (iii) into equation (i):

2(5y) - 3y = 7

10y - 3y = 7

7y = 7

y = 1

Now, from (iii): x = 5y = 5

x - y = 5 - 1 = 4