Represent the Solutions of a Linear Inequality or a System of Linear Inequalities Graphically as a Region of the Plane

If the solution to system of linear inequalities is a shaded region in a graph, what does this shaded region represent?

• The possible values that satisfy both inequalities

• The x-intercepts of the inequalities

• The impossible values that satisfy both inequalities

• The y-intercepts of the inequalities

Which of the following represents the feasible region of a system of linear inequalities?

• The x-intercepts of the inequalities

• The region outside the shaded area

• The region inside the shaded area

• The y-intercepts of the inequalities

The solution to a system of linear inequalities is always a region on the coordinate plane.

• True

• False

Graphically, the solution to a system of linear inequalities is the area where all shaded regions overlap.

• True

• False

The solution to a linear inequality in two variables often represents a ______ region on a coordinate plane.

Which of the following represents a system of linear inequalities in two variables?

• x + y ≤ 5

• 3x + 2y=10

• 2x − 3y > 7

• y ≥ 2x + 3

What does it mean if a point lies on the boundary line of a system of linear inequalities?

• It is a solution to the system

• It is part of the feasible region

• It is not a solution to the system

• It is an invalid point

What is the solution to the system of linear inequalities: y ≥ −2x+4 and y ≤ 3x+1 ?

• (−1,6)

• (0,4)

• (2,5)

• (3,7)

In a linear inequalities, shading the region that satisfies all the inequalities will give the feasible region.

• True

• False

To test which side of a line to shade when solving a linear inequality, we often use the point (0,0), also known as the _______.