Question 30336
x^2+y2=13   ----(1)
x^2+2y^2=14 ----(2)
That is (x^2+y^2)+y^2 = 14  ----(2)
putting (1) in (2)
13+y^2 =14
y^2 = 14-13
y^2 =1
y = +1 or y = -1 for which we get x^2 = 12
And x^2 = 12 implies x = +sqrt(12) and x = -sqrt(12)
Therefore there are four solutions
which is your choice (e) 4