If 2x2 + 8y = 121.5 and x2 - 8y = 121.5, then x =

2x² +8y = 121.5 
8y = 121.5 - 2x²
and,
x²-8y = 121.5 
-8y = 121.5 -x²
8y = x²-121.5 

Now, equate the two 8y's 

121.5-2x² = x² -121.5 
-3x² = -121.5-121.5 
-3x² = -243 
3x² = 243 
x² = 81 
x = ±9