Practice Graphing 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

What does it mean if a system of inequalities has an infinite number of solutions?

Back

It means that there are countless points that satisfy all inequalities in the system, typically represented by a shaded region on a graph.

Front

What is the graphical representation of a solution to a system of inequalities?

Back

The graphical representation is typically a shaded region on a coordinate plane, indicating all the possible solutions that satisfy the inequalities.

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 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 greater than or equal to the value on the right.

Front

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

Back

'>' does not include the boundary line, while '≥' includes the boundary line in the solution set.

Front

How do you graph the inequality y < x + 1?

Back

To graph y < x + 1, draw the line y = x + 1 as a dashed line (not including the line) and shade below the line.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set.

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set.