System of quadratic equations $x^2 + y = 4$ and $x + y^2 = 10$ How would you solve the following system of equations:
$$
x^2 + y = 4  \\
x + y^2 = 10
$$
Thanks very much!
I tried defining y in terms of x and then inserting in to the second equation:
$$
y = 4 - x^2  \\
x + (4 - x^2)^2 = 10
$$
Expand the second equation:
$$
 x + 16 - 8x^2 + x^4 = 10 
$$
Rearrange the terms:
$$
x^4 - 8x^2 +x + 6 = 0
$$
I tried factoring out this polynomial to simplify it for solving, but didn't succeed :( 

To solve general equations of the form $ax^4+bx^3+cx^2+dx+e=0$ requires quartic formula.
