3A Graphing systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which are the points that satisfy the inequality.

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 coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between '>' and '≥' in linear inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What is the significance of a dashed line in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (for inequalities using < or >).

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for inequalities using ≤ or ≥).

Front

How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.

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.

Front

What does it mean if a point lies outside the shaded region of a graph of linear inequalities?

Back

If a point lies outside the shaded region, it means that the point does not satisfy at least one of the inequalities in the system.

Front

How can you check if a point is in the solution set of a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is in the solution set.