We know that is a parabola, concave up, with vertex in the origin
So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.
Here's the examples:
- The horizontal line
intercepts the parabola twice: the system
is solved by
- The horizontal line
intercepts the parabola only once: the system is
which yields
which is a repeated solution
- The horizontal line
intercepts the parabola only once: the system is
which yields
which is impossible, because a squared number can't be negative.