Question

Solve for x and y: 

`5/x + 6y = 13, 3/x + 4y = 7`

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 = 15 in (i), we get:

`5/(1⁄3)  + 6y = 13`
25 + 6y = 13
6y = (13 – 25) = -12
y = -2
Hence, the required solution is x =` 1/5` and y = -2.