A linear-quadratic system is a system of equations containing one linear equation and one quadratic equation.
2x-y=3 x^2+y-3x=9
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. The values can be verified by substituting them 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.
