Question

1/2x + 1/3y=2
1/3x+1/2y=13/6

Answer 1

According to the Question

1/2x + 1/3y = 2 …………...(a)

1/3x + 1/2y = 13/6 …………...(b)

Assume,

1/x = s & 1/y = k

So,

From (a) we have,

s/2 + k/3 = 2

(3s + 2k)/6 = 2

3s + 2k = 2 × 6

3s + 2k = 12 …………..(c)

Also,

From (b) we have,

s/3 + k/2 = 13/6

(2s + 3k)/6 = 13/6

2s + 3k = 13/6 × 6

2s + 3k = 13 …………..(d)

Now,

Multiply (c) by 2 & (d) by 3

6s + 4k = 24 …………..(e)

6s + 9k = 39………..(f)

Now,

Subtract (f) from (e) we get,

-5k = -15

k = 15/5

k = 3

Substitute value of k in (c)

3s + 2k = 12

3s + 2 × 3 = 12

3s + 6 = 12

3s = 12 - 6

3s = 6

s = 6/3

s = 2

So,

1/x = s = 2

1/y = k = 3

Therefore,

x = 1/2 & y = 1/3