Linear Inequalities Review

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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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 does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, typically shown as a shaded region on one side of the boundary line.

Front

What is the difference between a solid line and a dashed line in the graph of 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

How do you graph a linear inequality in two variables?

Back

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

Front

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

Back

The solution set of a system of linear inequalities is the region where the shaded areas of all inequalities overlap, representing all points that satisfy all inequalities.

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 inequalities in the system simultaneously.

Front

How can you check if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What is the graphical representation of the inequality y < 2?

Back

The graphical representation is a horizontal line at y=2, with the area below the line shaded.