Systems of Inequalities

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

• It separates the solution region from the non-solution region.

• It indicates the maximum value of the function.

• It shows the slope of the inequality.

• It represents the intercepts of the graph.

What does the symbol '≥' represent in inequalities?

• It indicates that the value on the left is greater than or equal to the value on the right.

• It indicates that the value on the left is less than or equal to the value on the right.

• It indicates that the value on the left is greater than the value on the right.

• It indicates that the value on the left is equal to the value on the right.

What does the symbol '<' represent in inequalities?

• It indicates that the value on the left is greater than the value on the right.

• It indicates that the value on the left is equal to the value on the right.

• It indicates that the value on the left is less than the value on the right.

• It indicates that the value on the left is not equal to the value on the right.

What is the solution set of a system of inequalities?

• The set of all points that satisfy all inequalities in the system.

• The set of points that satisfy at least one inequality in the system.

• The set of points that do not satisfy any inequalities in the system.

• The set of points that are outside the boundaries of the inequalities.

What is the graphical representation of the solution to a system of inequalities?

• The overlapping shaded regions of the graphed inequalities.

• The individual lines of each inequality.

• The points where the inequalities intersect.

• The area outside the inequalities.

What does the symbol '>' represent in inequalities?

• It indicates that the value on the left is greater than the value on the right.

• It indicates that the value on the left is less than the value on the right.

• It indicates that the values on both sides are equal.

• It indicates that the value on the left is not equal to the value on the right.

What is an example of a system of inequalities?

• y < -x + 1 and y ≤ x - 4.

• y > -x - 1 and y ≥ x + 4.

• y = -x + 1 and y = x - 4.

• y ≥ -x + 1 and y < x + 4.

What is the role of test points in solving inequalities?

• Test points help determine which regions of the graph satisfy the inequality.

• Test points are used to calculate the slope of the graph.

• Test points indicate the maximum value of the inequality.

• Test points are irrelevant in solving inequalities.

How do you graph a linear inequality?

• 1. Graph the boundary line as a solid line if the inequality is '≥' or '≤', or as a dashed line if it is '>' or '<'. Shade the region that satisfies the inequality.

• 2. Always use a solid line for all inequalities and shade above the line.

• 3. Graph the boundary line as a dashed line for all inequalities and shade below the line.

• 4. Use a solid line for all inequalities and do not shade any region.

What is the first step in solving a system of inequalities by graphing?

• Identify the variables involved in the inequalities.

• Graph each inequality on the same coordinate plane.

• Calculate the intersection points of the inequalities.

• Convert the inequalities into equations.