Final answer:
Equations that can have infinite solutions include linear-linear, linear-quadratic, and quadratic-quadratic pairs, when two equations represent the same graph such as the same line or parabola.
Step-by-step explanation:
Types of equations that can have infinite solutions include linear-linear, linear-quadratic, and quadratic-quadratic pairs of equations. For example, in the case of two linear equations (y = mx + b), if they represent the same line, they will have the same slope (m) and y-intercept (b), resulting in infinite solutions as every point on the line is a solution to both equations. Comparatively, a linear equation and a quadratic equation will usually have up to two intersection points, but can also coincide at all points if the quadratic is the square of the linear equation, forming a parabola that touches the line at every point.
In cases of quadratic-quadratic pairs, it is possible for both parabolas to be identical, in which case every point on one parabola will be a solution to the other, again resulting in infinite solutions. However, typically quadratic equations will intersect at zero, one, or two points.