Solutions to Systems of Inequalities- Graphs!

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

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 it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of the shaded regions of the inequalities on a coordinate plane, where the overlapping shaded area represents the solution set.

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 a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Then shade the appropriate region.

Front

What is the significance of the shaded region in the graph of a system of inequalities?

Back

The shaded region represents all the possible solutions to the system of inequalities.