Question

If 4x + 6y = 3xy and 8x + 9y = 5xy then

Options

• x = 2, y = 3

• x = 1, y = 2

• x = 3, y = 4

• x = 1, y = –1

Answer 1

x = 3, y = 4

Explanation:

From 4x + 6y = 3xy

⇒ x(3y – 4) = 6y

⇒ `x = (6y)/(3y - 4)`

From 8x + 9y = 5xy

⇒ x(5y – 8) = 9y 

⇒ `x = (9y)/(5y - 8)`

Equate the two expressions and cancel y ≠ 0: 

6(5y – 8) = 9(3y – 4)

⇒ 30y – 48 = 27y – 36

⇒ 3y = 12

⇒ y = 4

Then `x = (6 xx 4)/(3 xx 4 - 4)`

= `24/8`

= 3