Question

Define the solution to a system of linear inequalities.

Answer 1

The solution to a system of linear inequalities is the set of values that satisfy all the inequalities at once, graphically represented as the overlapping shaded region on a coordinate plane.

Step-by-step explanation:

The solution to a system of linear inequalities is defined as the set of values that satisfy all inequalities in the system simultaneously. To find this solution set, each inequality is graphed on the same coordinate plane to determine the region where all inequalities overlap. Within this region, any point represents a solution to the system. If an inequality is non-strict (less than or equal to or greater than or equal to), the boundary line is included in the solution set and is usually drawn as a solid line. If the inequality is strict (less than or greater than), the boundary line is not included in the solution set and is depicted as a dashed line. The solutions are typically represented graphically by shading the area of the plane that satisfies all conditions.

Answer 2

Systems of inequalities can be graphs on a coordinate plane. The solution of a linear inequality is the ordered pair that is a solution to all inequalities. When two inequalities within a system share no common region, then the system has no solution and no specific point will be a solution set to both inequalities.