Systems 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

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

Back

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

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 graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Front

What does the symbol '>' indicate in an inequality?

Back

'>' indicates that the value on the left is greater than the value on the right.

Front

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

Back

'<'' indicates that the value on the left is less than the value on the right.

Front

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

Back

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

Front

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

Back

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

Front

How do you graph the inequality y > 2x - 4?

Back

To graph y > 2x - 4, first graph the line y = 2x - 4 as a dashed line (not including the line), then shade above the line.

Front

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

Back

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