Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the solution to a system of inequalities represent?

Back

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

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

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. It helps to identify the solution set.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

The inequality y < 2x + 3 represents the region below the line y = 2x + 3, excluding the line itself.

Front

What is the graphical representation of the inequality x > -3?

Back

The inequality x > -3 is represented by a vertical dashed line at x = -3, with the region to the right of the line shaded.

Front

How do you solve a system of inequalities by graphing?

Back

To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph where all constraints (inequalities) are satisfied. It is typically bounded by the lines representing the inequalities.