Question

If 2/x+ 3/y =13 and 5/x- 4/y = -2, then x+y equals (a) 1/6 (b) -1/6 (c) 5/6 (d) -5/6

Answer 1

c

Explanation:

Let 1/x = a &

1/y = b

So, now the equation:

2a +3b = 13 --------------------(i)

5a - 4b = -2 --------------------(ii)

To eliminate a, Multiply equation (i) by 5 and multiply (ii) by (-2)

(i)*5 10a + 15b = 65

(ii)*(-2) - 10a + 8b = 4 ( Now add, a will be eliminated}

23b = 69

b= 69/23

b = 3

Plug in the value of b in equation (i)

2a + 3*3 = 13

2a + 9 = 13

2a = 13 - 9

2a = 4

a= 4/2

a = 2

Now a = 1/x ------>x = 1/a = 1/2

b = 1/y ----------->y = 1/b = 1/3

`x+y=(1)/(2)+(1)/(3)\\\\=(1*3)/(2*3)+(1*2)/(3*2)\\\\=(3)/(6)+(2)/(6)\\\\=(5)/(6)`