Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the region defined by the inequalities.

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

What does shading above a line in a graph of an inequality represent?

Back

Shading above a line represents the region where the inequality is true for greater than (>) or greater than or equal to (≥) the line.

Front

What does shading below a line in a graph of an inequality represent?

Back

Shading below a line represents the region where the inequality is true for less than (<) or less than or equal to (≤) the line.

Front

How can you graph the inequality y < 2x + 3?

Back

First, graph the line y = 2x + 3 as a dashed line. Then, shade the area below the line to represent all points where y is less than 2x + 3.

Front

What is the solution set of the system of inequalities y > x and y < 3?

Back

The solution set is the region above the line y = x and below the line y = 3, excluding the lines themselves.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it may or may not be included in the solution set, depending on whether the inequality is strict (>) or non-strict (≥).

Front

What is the graphical representation of the inequality y ≤ -x + 4?

Back

Graph the line y = -x + 4 as a solid line and shade below the line to represent all points where y is less than or equal to -x + 4.