Systems of Inequalities HW

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 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 does it mean to graph a system of inequalities?

Back

Graphing a system of inequalities involves plotting each inequality on the same coordinate plane and identifying the region where all shaded areas overlap, which represents the solution set.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (>, <), the line is dashed; if it is inclusive (≥, ≤), the line is solid.

Front

How do you rewrite an inequality in 'y=' form?

Back

To rewrite an inequality in 'y=' form, isolate y on one side of the inequality. For example, from 3x - 6y > 12, you would rearrange it to y < (1/2)x - 2.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it may or may not be included in the solution set, depending on whether the inequality is strict or inclusive.

Front

How can you check if a point is a solution to a specific inequality?

Back

Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

Front

What is the difference between a strict inequality and an inclusive inequality?

Back

A strict inequality (< or >) does not include the boundary line, while an inclusive inequality (≤ or ≥) includes the boundary line in the solution set.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph of y < 2x + 3 is a dashed line representing y = 2x + 3, with the area below the line shaded to indicate all points where y is less than 2x + 3.