A linear-quadratic system is a system of equations containing one linear equation and one quadratic equation. Similar to a system of linear equations, the solutions to a linear-quadratic system are the values that satisfy both equations simultaneously. For instance, in the given example $x=4$ and $y=5$ are solutions. This can be verified by substituting these values into each equation.

$2x-y=3$	$x^2+y-3x=9$
$2(4)-5=3$	$4^2+5-3(4)=9$
$8-5=3$	$16+5-12=9$
$3=3✓$	$9=9✓$

In the example, since the equations remain true, the values are a solution of the linear-quadratic system. The graph of the linear equation is a straight line, and that of the quadratic equation is a parabola. These graphs can have $0,$ $1,$ or $2$ points of intersection. Therefore, the number of solutions for a linear-quadratic system is also $0,$ $1,$ or $2.$ A linear-quadratic system can be solved both algebraically and graphically. Since this system includes a quadratic equation, it is a nonlinear system.