Question

Solve for x and y:
`3/x + 2/y = 12, 2/x + 3/y = 13`

Answer 1

The given equations are:
`3/x + 2/y = 12`    ……..(i)
`2/x + 3/y = 13 ` ……..(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting (ii) from (i), we get:
`9/x - 4/x = 36 – 26`
`⇒5/x = 10`
`⇒x = 5/10 = 1/2`
Now, substituting x = `1/2 `in (i), we have
`6 + 2/y = 12`
`⇒2/y = 6`
⇒`y = 1/3`

Hence, `x = 1/2 and y = 1/3`.