System of Linear Inequalities

Front

What is a system of linear inequalities?

Back

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

Front

What does it mean for a line to be solid in a graph of inequalities?

Back

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

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of y > 2x - 4 look like?

Back

The graph of y > 2x - 4 is a dashed line representing the boundary where y equals 2x - 4, with the area above the line shaded to indicate all points where y is greater than 2x - 4.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the inequality. Points within this region satisfy the inequality.

Front

What does the inequality y < 2 represent on a graph?

Back

The inequality y < 2 represents a horizontal line at y = 2, with the area below the line shaded, indicating all points where y is less than 2.

Front

How can you graph the system of inequalities y < 2 and y > 2x - 4?

Back

Graph the line y = 2 as a solid line and shade below it. Then graph y = 2x - 4 as a dashed line and shade above it. The solution is where the shaded regions overlap.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions to the system.

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 of an inequality, it may or may not be included in the solution set, depending on whether the inequality is strict (>) or inclusive (≥).