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 a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

Front

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

Back

The solution set represents all the points (x, y) that satisfy all inequalities in the system.

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 (≤ or ≥), while a dashed line indicates that points on the line are not included ( < 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when substituted into it.

Front

What is the graphical representation of y ≤ 3x?

Back

The graph of y ≤ 3x is a solid line with a slope of 3, and the region below the line is shaded.

Front

What is the graphical representation of y > -2x + 4?

Back

The graph of y > -2x + 4 is a dashed line with a slope of -2, and the region above the line is shaded.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Front

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

Back

The boundary line separates the solution set from the non-solution set. Points on the line may or may not be included in the solution, depending on whether the inequality is strict or inclusive.