Linear Inequality SYSTEMs

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 (>, <, ≥, ≤).

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 inequalities in the system simultaneously.

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

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

Back

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

Front

What does the solution set of a system of linear inequalities represent?

Back

The solution set represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

Front

How can you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a line. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region that satisfies the inequality.

Front

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

Back

The boundary line divides the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

What does the term 'system of inequalities' refer to?

Back

A system of inequalities consists of two or more inequalities that are considered together, and the solution is the intersection of the solution sets of each inequality.

Front

How do you identify a point that is NOT a solution to a system of inequalities?

Back

A point is NOT a solution if it fails to satisfy at least one of the inequalities in the system.

Front

What is the graphical representation of the inequality y ≤ 2x - 1?

Back

The graph includes the line y = 2x - 1 (solid line) and the region below the line.