Question 89877
FIRST I WOULD PLOT THEM & SEE IF THERE IS ANY OBVIOUS SOLUTION.
{{{ graph( 300, 200, -6, 5, -10, 10, y = x, y^2 = -x^2 +4) }}} (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = x and y^2 = -x^2 
+4). 
OR SET X=Y & SOLE FOR Y IN THE FIRST EQUATION
Y^2+Y^2=4
2Y^2=4
Y^2=4/2
Y^2=2
Y=+/-1.414 ANSWER.
X=Y=+/-1.414 ANSWER.