Graphing Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does it mean when a system of linear inequalities has no solution?

Back

It means that the graphs of the inequalities do not intersect at any point, indicating that there are no values that satisfy all inequalities simultaneously.

Front

What symbols indicate a solid line when graphing inequalities?

Back

The symbols ≤ and ≥ indicate a solid line when graphing inequalities.

Front

What symbols indicate a dashed line when graphing inequalities?

Back

The symbols < and > indicate a dashed line when graphing inequalities.

Front

How do you rewrite the inequality 3x - 6y > 12 in 'y=' form?

Back

y < (1/2)x - 2.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where all inequalities in the system are true.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

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

Front

What is the graphical representation of the inequality y ≥ 2x + 1?

Back

The graph will have a solid line for y = 2x + 1 and shade above the line.

Front

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

Back

A boundary point is a point on the line that separates the solution region from the non-solution region.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities, forming the solution region.