Answer
There is no solution between the 2 equations.
See Graph I for the graphing.
Work Step by Step
$x^2 + 2y^2 = 2 \longrightarrow (i)$
$x - y = 2 \longrightarrow (ii)$
From $(ii)$, we have
$x - y = 2$
$x = y + 2 \longrightarrow (iii)$
Sub. $(iii)$ into $(i)$, we have
$(y + 2)^2 + 2y^2 = 2$
$y^2 + 4y + 4 + 2y^2 = 2$
$3y^2 + 4y + 2 = 0$
By means of quadratic formula, since Discriminant D = $4^2$ - 4x3x2 = -8 (less than 0), there will be no real roots with $y$, and therefore, there is no intersection between the 2 equations.
See Graph I for the graphing.