Question

Solve by cross-multiplication method

`2/x + 3/y` = 5,  `3/x - 1/y + 9` = 0

Answer 1

`1/x` = a, `1/y` = b

2a + 3b – 5 = 0 → (1)

3a – b + 9 = 0 → (2)

Using the coefficients for cross multiplication

`"a"/(27 - (5)) = "b"/(-15 - (18)) = "c"/(-2 - (9))`

`"a"/22 = "b"/(-33) = 1/(-11)`

`"a"/22 = 1/(-11)`

–11a = 22

a = `(-22)/11` = – 2

`"b"/(-33) = 1/(-11)`

– 11b = – 33

11b = 33

b = `33/11` = 3

But `1/x` = a ⇒ `1/x` = – 2

– 2x = 1 ⇒ 2x = – 1

x = `-1/2`

but `1/y` = b

`1/y` = 3 ⇒ 3y = 1

y = `1/3`

∴ The value of x = `-1/2` and y = `1/3`