Question

1. what does it mean if a system of equations has infinitely many solutions?

a. the equations are the same line
b. the equations intersect at multiple points
c. the equations do not intersect
d. the equations are perpendicular

1. when considering the graphical representation of a consistent and dependent system, what will the graph look like?

a. two intersecting lines at several points.
b. two parallel lines that do not intersect.
c. two perpendicular lines that intersect at one point.
d. one line, as both equations graph to the same line.

Explanation:

1. A system with infinitely many solutions means all points satisfy both equations, which occurs when the equations represent the exact same line.
2. A consistent dependent system has infinitely many solutions, so both equations graph as a single overlapping line.

Answer:

1. a. The equations are the same line
2. d. One line, as both equations graph to the same line.