Systems of Inequality Constraints

The _____________________________ is the intersection of the solutions to each inequality. Every point in the intersection region satisfies all inequalities in the system.

• System of Linear Equations

• Consistent Systems

• Inconsistent Systems

• Solution of a System of Linear Inequalities

In a system of linear inequalities, the inequalities are known as _____________ because the values of the expressions are “constrained” to lie within a certain region on the graph.

• Linear Combination Method

• Half-plane

• Boundary line

• Constraints

A ______________, determined by the inequality in a linear inequality, divides the plane into two half-planes and the inequality symbol indicates which half-plane contains all the solutions.

• Linear Combination Method

• Half-plane

• Boundary line

• Constraints

Two or more inequalities that represent the constraints in the same situation.

• system of inequalities

• system of equations

• equations

• expressions

Answer explanation

Two or more inequalities that represent the constraints in the same situation form a system of inequalities.

All pairs of values that make the inequalities in a system true are solutions to the system. This can be represented by the points in the region where the graphs overlap.

• solutions to a system of inequalities

• system of inequalities

• system of equations

• variables

Answer explanation

Solutions to a system of inequalities are all pairs of values that make the inequalities in a system true are solutions to the system. The solutions to a system of inequalities can be represented by the points in the region where the graphs of the two inequalities overlap.

A limitation on the possible values of variables in a mode, often expressed by an equation or inequality or by specifying that the value must be an integer.

• constraint

• model

• constant of proportionality

• representation

Answer explanation

A constraint is a limitation on the possible values of variables in a mode, often expressed by an equation or inequality or by specifying that the value must be an integer.

For example, distance above the ground, d, in meters, might be constrained to be non-negative, expressed by d is greater than or equal to 0.

Which of the following points is a solution to the system of inequalities?

• (5,2)

• (-4,-4)

• (1,-5)

Which of the following points is a solution to the system of inequalities?

• (0,0)

• (4,10)

• (6,-4)

• The system has no solutions.

Given the system of inequalities, which of the following points is a solution to the system.

• (3,1)

• (4,2)

• (5,3)

Which of the following inequalities is represented by the graph?