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 linear inequalities?

Back

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

Front

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

Back

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

Front

How do you determine if a point is a solution to an 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 does shading above a line indicate in graphing inequalities?

Back

Shading above a line indicates that the solution set includes all points where the y-value is greater than the line (y > mx + b).

Front

What does shading below a line indicate in graphing inequalities?

Back

Shading below a line indicates that the solution set includes all points where the y-value is less than the line (y < mx + b).

Front

What is the significance of boundary lines in a system of linear inequalities?

Back

Boundary lines separate the solution set from the non-solution set. Points on the boundary line may or may not be included in the solution set, depending on whether the line is solid or dashed.

Front

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

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to represent all points where y is less than 2x + 3.

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, it may be included in the solution set if the line is solid, but not included if the line is dashed.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.