Unit 4 Rev Systems

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

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

How do you determine the solution to a system of equations?

Back

The solution to a system of equations is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The graph of y < x - 2 is a dashed line with a slope of 1, and the area below the line is shaded to represent all points where y is less than x - 2.

Front

What does the inequality y ≥ x + 4 indicate about the graph?

Back

The graph of y ≥ x + 4 includes a solid line with a slope of 1, and the area above the line is shaded to represent all points where y is greater than or equal to x + 4.

Front

How do you graph the inequality y < -x + 2?

Back

To graph y < -x + 2, draw a dashed line for y = -x + 2 and shade below the line to indicate all points where y is less than -x + 2.

Front

What is the solution to the system of inequalities y > -x - 1 and y ≥ x + 4?

Back

The solution is the region where the graphs of both inequalities overlap, which includes points above the line y = -x - 1 and on or above the line y = x + 4.

Front

What does the term 'feasible region' refer to in the context of inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied, representing all possible solutions.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph, check the slope and y-intercept of the line, determine if it should be solid or dashed, and shade the appropriate region based on the inequality.