If x+y=10 and x-y=4 find the value of x2 y2

The answer is:  1323 .

Explanation:

If  x + y = 10 ;  then:  x = 10 - y ;  and y = 10 - x ;

If  x - y = 4 ; then x = 4 + y ;


   Start with:  "x + y = 10" ; 

Substitute "(4+y)" for "x" ;

       (4+y) + y = 10 ; 

         4 + 2y = 10 ; subtract "4" from each side of the equation:

   4 + 2y - 4 = 10 - 4 ;

              2y = 6 ; divide each side of the equation by "2" ; to isolate "y" on one side of the equation; and to solve for "y"; 

              2y/2 = 6/2 ;

 to get:      y = 3 ;


Since:  x + y = 10 ;  substitute "3" for "y"; and solve for "x" :

           x + 3 = 10 ;  subtract "3" from each side of the equation:

           x + 3 - 3 = 10 - 3 ;

  to get:   x = 7 ;

Now, the question asks:  what is: x² * y² ?  
 
                     x² * y²  =  7² * 3³ = 49 * 27 = 1323 .