System of Inequality

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 the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either larger than or equal to the value on the right.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

Front

How do you graph the inequality y < 3?

Back

To graph y < 3, draw a horizontal dashed line at y = 3. Shade the area below the line to represent all points where y is less than 3.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How can 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 is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It contains all points that satisfy all inequalities in 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 is included in the solution set if the inequality is '≥' or '≤', but not if it is '>' or '<'.