If you are describing a graph that consists of a parabola and a line that intersect at two points, would the system be dependent and consistent. Or is dependent only used if the system has an infinite amount of solutions?
Thanks!
When describing a system of equations, such as a graph consisting of a parabola and a line that intersect at two points, we can determine if the system is dependent and consistent.
A system of equations is considered dependent when there are infinitely many solutions. This means that the equations represent the same line or have overlapping graphs. In such a case, any value that satisfies one equation will also satisfy the other equation.
On the other hand, a system of equations is considered consistent when there is a unique solution or a finite number of solutions. This implies that the equations represent distinct lines or graphs that intersect at a specific point or points.
In the scenario you described, with a parabola and a line intersecting at two points, the system is dependent and consistent. The reason for this is that a parabola and a line generally have different shapes and slopes, so they intersect at distinct points. The fact that they intersect at two points means that there are a finite number of solutions, making the system consistent. Additionally, since the parabola and line do intersect, they are dependent on each other.
To summarize, the system of equations consisting of a parabola and a line intersecting at two points is dependent and consistent because there are a finite number of solutions where the equations overlap or intersect.