1A Graphing systems of Linear Inequalities

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 (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it lies in the shaded region of the graph representing the solution set of the inequalities.

Front

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

Back

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

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

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

Back

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

Front

What does it mean for a system of inequalities to have no solution?

Back

A system of inequalities has no solution if the shaded regions do not overlap, meaning there are no points that satisfy all inequalities.

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

How do you write the inequality for a given graph?

Back

To write the inequality, identify the slope and y-intercept of the boundary line and determine whether the region above or below the line is shaded.

Front

What does it mean for a system of inequalities to have infinitely many solutions?

Back

A system has infinitely many solutions if there are an infinite number of points in the overlapping shaded region that satisfy all inequalities.