Why Is HashCode Needed For Checking Duplicates In HashMap And Set

The keys in a HashMap and the values in a Set must all be unique, but this can be circumvented when using custom objects in a HashMap and Set, because the compiler has no way to determine if the objects are equal or not, as shown in the example below:

Java Code:

import java.util.LinkedHashMap;
import java.util.Map;
public class HashCodeEquals {
public void run(){
Person p1 = new Person(1, "John");
Person p2 = new Person(2, "Matt");
Person p3 = new Person(1, "John");

[code]....

Obviously the equals method is needed because that compares the two objects. But why is the hashCode method needed?