Could a system of two equations that includes a linear equation and a Quadratic equation ever have an infinite number of solutions? If so how could you tell from the graph? If not explain why.
No, a system of two equations that includes a linear equation and a quadratic equation cannot have an infinite number of solutions.
A linear equation represents a straight line on a graph, while a quadratic equation represents a parabola. These two types of graphs will intersect at most twice, meaning they can have at most two solutions.
If a linear equation and a quadratic equation have an infinite number of solutions, it would mean that the straight line and the parabola coincide, which is not possible. The only way for a system of equations to have an infinite number of solutions is if the equations are equivalent, meaning they represent the same line or curve. This would require both equations to be linear or both equations to be quadratic.
Therefore, if you graph a system of equations involving a linear equation and a quadratic equation, you will see either two intersection points or no intersection points, but never an infinite number of intersection points.