Quadratic simultaneous equations combine a quadratic equation with another equation, often a line. A solution is an ordered pair $(x,y)$ that makes both equations true at the same time.

On a graph, the solution pairs are the intersection points of the two graphs. That is why there can be $0$, $1$, or $2$ real solutions.

A linear equation such as $3x+y=5$ has variables only to the first power, so it draws as a straight line. A quadratic equation such as $x^2+y^2=25$ contains a squared term, so its graph is curved.