Show / Hide Component In VisualForce Page

Controller Code :-

public class popup
{
  public boolean ShowPopup {get; set;}

  public void HidePopup()
  {
    ShowPopup= false;
  }

  public void showPopup()
  {
    ShowPopup= true;
  }
}

VisualForce Page :-

<apex:page controller="popup">
   <apex:form >
     <B>
    <apex:commandlink value="Display Second Link" action="{!showPopup}"/>
    </B><br></br><br></br>
    <apex:outputPanel layout="block" rendered="{!ShowPopup}">
     <apex:commandlink value="Click Me To Hide This Link" action="{!HidePopup}"/>
    </apex:outputPanel>
   </apex:form>
</apex:page>

OutPut Screen 1:-

OutPut Screen 2 :-