If the income elasticity of demand for good x is negative and the cross-price elasticity of demand between good x and good y is negative, which of the following must be true of good x

Good X is Inferior Good, Good X is complementary good of Good Y.

Explanation:

Demand : Buyers ability & willingness to buy given price - has 4 factors (price of good, income, price of related goods, Taste).

Based on Income : Normal Goods demand vary directly with Income, more demand at higher income & vice versa. Eg: Normal grains like Wheat, Rice. Inferior Goods demand vary inversely with Income, more demand at lower income & vice versa. Eg: Low grade, cheap grains like Bajra.

Price of Related Goods: Related Goods can be Substitutes or Complements.  Substitute (interchangeable) goods price are directly related a with good's demand because - substitute price rise makes the good relatively cheap, increases its demand & vice versa. Complementary (together used) goods price are inversely related with a good's demand because - complements price rise makes the product combination expensive, decreases its demand & viceversa. 1st eg: Coke, Pepsi ; 2nd eg: Tea, Sugar.

If income elasticity of demand for good X is negative : implies it varies inversely with Income - It is an Inferior Good

If Cross Price Elasticity of demand between good X and good Y is negative : Implies Y's prices & X's demand vary inversely - Both are complements of each other.

answer; by looking at total product,marginal product,and changes in both after changes in inputs