If the consumer wants to stay on the same level of satisfaction, it is important that

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Quantity of both commodities$-$ x and y must remain same throughout the curve.

if quantity of one commodity $($x$)$ rises then quantity of another commodity $($y$)$ must fall

If quantity of one commodity $($x$)$ fails then quantity of another commodity $($y$),$ must remain constant

if quantity of one commodity $($x$)$ rises then quantity of another commodity $($y$)$ must also rise