Question

You suspect that a system of two equations does NOT have a solution. If you were to graph the system on a coordinate plane, what would you expect the graph to look like?

a. Two parallel lines
b. A single point
c. A line intersecting a point
d. A circle

Answer 1

When graphing two linear equations that do not have a solution, they appear as two parallel lines on a coordinate plane, indicating they have the same slope but will never intersect.

Step-by-step explanation:

If a system of two equations is graphed and does not have a solution, this implies that the two lines will never intersect. In the context of a coordinate plane, this situation is represented by two parallel lines. These parallel lines could either be horizontal, having a slope of zero, or they could have identical slopes if they are not horizontal. Nonetheless, the defining feature is that the lines have the same slope and different y-intercepts, meaning they will never cross each other and hence the system of equations has no solutions (the system is inconsistent).