Why Eutectic point occurs at low temperature?

Dear Syudent,

Consider a simple two metal ( or other substance) system with metals A and B.

There are only three points on the melting temperature v composition diagram that where a single substance occurs.

These are 
Pure A
Pure B
The Eutectic point.

At all other compositions there is more than one substance present. Hence the result is a mixture.

Either Eutectic plus excess A or Eutectic plus excess B.

Elementary physics tells us that

A single pure substance has a well defined single melting point.
A mixture of substances melts over a range of temperature, determined by the components of the mixture.

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