Graphing 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

How do you graph a system of inequalities?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies each inequality. 4. The solution is where the shaded regions overlap.

Front

What does the symbol '>' mean in inequalities?

Back

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

Front

What does the symbol '<' mean in inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' 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 '≤' mean in inequalities?

Back

'≤' 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 determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

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

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 <).

Front

How can you identify the solution set of a system of inequalities graphically?

Back

The solution set is the area where the shaded regions of all inequalities overlap on the graph.