Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

Front

What does the symbol '>' represent in inequalities?

Back

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

Front

What does the symbol '<' represent in inequalities?

Back

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

Front

What does the symbol '≥' represent in inequalities?

Back

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

Front

What does the symbol '≤' represent in inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as a solid line if the inequality is '≥' or '≤', or as a dashed line if it is '>' or '<'. 2. Shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

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

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 significance of the boundary line in a graph of inequalities?

Back

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

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

It means that the point satisfies the inequality if the line is solid (≥ or ≤) but does not satisfy it if the line is dashed (> or <).