What is a system of linear inequalities?

A system of linear inequalities refers specifically to a collection of inequalities in which all expressions are linear. This means that each inequality is made up of linear functions, which are defined by equations of the form ( ax + by + c \geq 0 ) or ( ax + by + c \leq 0 ), where ( a ), ( b ), and ( c ) are constants and ( x ) and ( y ) are variables. The region defined by these inequalities on a graph represents all the possible solutions that satisfy all the inequalities in the system simultaneously.

The emphasis on linearity is crucial, as nonlinear expressions or quadratic terms would disqualify the set from being termed a "system of linear inequalities." Thus, the correct answer highlights the specific nature of these inequalities, which distinguishes them from systems that might involve more complex expressions. This clarity ensures that when solving or graphing these inequalities, one understands that the relationships are linear and can often be represented in a coordinate plane with straight lines and shading to indicate solution sets.