Systems of Inequalities

Front

What is a system of inequalities?

Back

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

Front

How do you graph an inequality in two variables?

Back

To graph an inequality in two variables, first graph the corresponding equation as if it were an equality. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, 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 '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to. The former does not include the boundary line, while the latter does.

Front

What does it mean if a point is in the solution set of a system of inequalities?

Back

If a point is in the solution set, it means that the coordinates of that point satisfy all inequalities in the system.

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 graphical representation of the inequality x < -3?

Back

The graphical representation of x < -3 is a vertical dashed line at x = -3, with the region to the left shaded.

Front

What does the shaded region in a graph of inequalities indicate?

Back

The shaded region indicates all the possible solutions that satisfy the inequality or system of inequalities.

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 the significance of a dashed line in graphing inequalities?

Back

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