Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities with the same variables.

Front

How do you represent a linear inequality graphically?

Back

By shading the region that satisfies the inequality and using a solid or dotted line to indicate whether the boundary is included.

Front

What does a dotted line indicate when graphing an inequality?

Back

It indicates that the points on the line are not included in the solution (used for < or >).

Front

What does a solid line indicate when graphing an inequality?

Back

It indicates that the points on the line are included in the solution (used for ≤ or ≥).

Front

How do you solve a system of linear inequalities by graphing?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region.

Front

What is the solution to the system of inequalities y > -x - 1 and y ≥ x + 4?

Back

The solution is the region above the line y = -x - 1 and on or above the line y = x + 4.

Front

What is the significance of the boundary line in a linear inequality?

Back

It separates the solution set from the non-solution set.

Front

In the context of inequalities, what does the term 'feasible region' refer to?

Back

The area on the graph where all the inequalities overlap, representing all possible solutions.

Front

How can you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives, then express them as inequalities.

Front

What is the graphical representation of the inequality y < ⅓ x + 3?

Back

A shaded region below the line y = ⅓ x + 3, with a dotted line.