Is the system supposed to be the following?
x2 + 2y2 = 2
x - y = 2
If so, graphing the system shows an ellipse with a line outside of it; they do not intersect, therefore no solution.
To solve it algebraically, solve the linear equation for either variable: x = y + 2
Substitute y+2 into the first equation:
(y + 2)2 + 2y2 = 2
y2 + 4y + 4 + 2y2 = 2
3y2 + 4y + 2 = 0
Using the quadratic formula results in a negative number under the square root sign; therefore, there is no real number solution.
Hope this helps!