Question

Solve for x and y: 

`5/x + 6y = 13, 3/x + 4y = 7 (x ≠ 0)`

Answer 1

The given equations are:

`5/x + 6y = 13`   ...(i)

`3/x + 4y = 7`   ...(ii)

Putting `1/x = u`, we get:

5u + 6y = 13   ...(iii)

3u + 4y = 7   ...(iv)

On multiplying (iii) by 4 and (iv) by 6, we get:

20u + 24y = 52   ...(v)

18u + 24y = 42   ...(vi)

On subtracting (vi) from (v), we get:

2u = 10 ⇒ u = 5

⇒ `1/x = 5 ⇒ x = 1/5`

On substituting `x = 1/5` in (i), we get:

`5/(1/3) + 6y = 13`

25 + 6y = 13

6y = (13 – 25)

6y = –12

y = –2

Hence, the required solution is `x = 1/5` and y = –2.