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 the symbol '>' represent 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 '<' represent 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 '≥' represent 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 '≤' represent 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 graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. 3. Shade the region that satisfies the inequality.

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.

Front

What does 'y > 2x - 4' represent graphically?

Back

It represents the area above the line y = 2x - 4, not including the line itself.

Front

What does 'y < 2' represent graphically?

Back

It represents the area below the horizontal line y = 2, not including the line itself.

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.