how do you solve this by using addition method

Question

x^2+y^2=36

y^2-4x=36

Answer 1

x^2   +    y^2                =     36
          -     y^2   +  4x    =   - 36           [second equation times (-1)]

----------------------------------------     [elimination; add equations]

x^2                    + 4x     =     0

 

     x(x+4) = 0

  Either x=0 or (x+4=0) or both           [Multiplicative Property of Zero]

 

  Either x=0 or x=-4

     Solutions:  (0,6) and (-4,2√5)