System 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 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 a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, typically shown as a shaded region on one side of the line.

Front

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

Back

'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary line.

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 is a solution if the inequality is '≥' or '≤', but not if the inequality is '>' or '<'.

Front

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

Back

Graph the line y = 2x - 4 as a dashed line (since it's '>') and shade above it. Then graph y = 2 as a solid line and shade below it.

Front

What is the significance of a dashed line in the graph of an inequality?

Back

A dashed line indicates that points on the line are not included in the solution set (used for '>' or '<').

Front

What is the significance of a solid line in the graph of an inequality?

Back

A solid line indicates that points on the line are included in the solution set (used for '≥' or '≤').

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 region represents the solution set.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system simultaneously.