If 5x - 13xy + 6y = 0, find x : y.
We'll simplify 5x² - 13xy + 6y2 = 0, by splitting the xy term 5x2 -10xy - 3xy + 6y2 = 0 = 5x (x-2y) - 3y (x-2y) = 0 = (5x-3y) (x – 2y) = 0 Taking, ⇒ 5x - 3y = 0 ⇒ 5x = 3y ⇒ x: y = 3:5 Taking, ⇒ x - 2y = 0 ⇒ x = 2y ⇒ x: y = 2:1 Finally x:y =3:5 or 2:1
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