If a·x = b·y (with a, b ≠ 0), then which relation is correct?

Given data

• a·x = b·y, with a and b nonzero.

Concept / Approach

• Simple proportion: if products are equal, variables are in inverse ratio to coefficients.

Step-by-step calculation

a·x = b·y ⇒ divide both sides by a·y: (x / y) = (b / a)Therefore, x : y = b : ax : y = b : a

Verification

Example: let a = 2, b = 3, choose x : y = 3 : 2 ⇒ LHS = 2·3 = 6; RHS = 3·2 = 6.

Common pitfalls

• Writing x : y = a : b (that would imply a·x and b·y are not equal unless a = b).

Final Answer

x : y = b : a