Question

a system of ______________ consists of two or more inequalities that work together to define the limits of a scenario.
the area where the shaded regions of all inequalities overlap on the graph represents the ______________ region.
a boundary line is represented as a ______________ line if the inequality includes the boundary in the solution set.
a ______________ line is used to represent a boundary that is not included in the solution set of an inequality.
inequalities that use the symbols < or > indicate that the boundary line is ______________ from the solution set.
the ______________ of inequalities is used in linear programming to determine feasible solutions to problems involving constraints.
graphing each inequality on the same coordinate plane helps visualize the ______________ region where all conditions are satisfied.

Explanation:

1. First blank:

A system of linear inequalities consists of two or more linear inequalities working together to define limits. The key term here is "linear inequalities" as the context is about inequalities defining a scenario's limits, and linear inequalities are systems with multiple inequalities.

When graphing multiple inequalities, the overlapping shaded region (where all inequalities are satisfied) is called the feasible region. This is a key concept in systems of inequalities, especially in linear programming, where feasible region represents the set of all possible solutions.

If an inequality includes the boundary (e.g., $\leq$ or $\geq$), the boundary line is drawn as a solid line. This is a standard convention in graphing inequalities: solid lines mean the boundary is part of the solution set.

Answer:

linear inequalities

2. Second blank: