valency of carbide is C^4-and of calcium is Ca^2+.But why is the formula of calcium carbide CaC₂and not Ca₂C ????

CaC2 is an ionic compound and is made up of Ca²⁺ and C₂ ^2-(carbide anion)

Carbon carry 4 electron in its valence shell. Out of this 4 electrons 3 is used in making triple bond with other carbon and is left as such.Therefore in carbide anion there is triple bond exist between two carbon so each carbon carry 7 electrons(6 from 3 bonds and a single electron).Now both the carbon can accept one electron to complete its octet.That is why it has overall -2 charge.he structure of carbide shown below:

Since cation has +2 and anion has -2 charge there molecular formula will show the ratio of cation and anion is 1: 1 that is why CaC₂.