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

Answer:

c

Step-by-step 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

$x+y=\frac{1}{2}+\frac{1}{3}\\\\=\frac{1*3}{2*3}+\frac{1*2}{3*2}\\\\=\frac{3}{6}+\frac{2}{6}\\\\=\frac{5}{6}$