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

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, determine the shading for each inequality (above or below the line) and find the overlapping region that satisfies all inequalities.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the value can be less than or equal to the number.

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to the number.

Front

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

Back

'>' means 'greater than' (not including the number), while '≥' means 'greater than or equal to' (including the number).

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 is the graphical representation of the inequality y < 2x + 3?

Back

The graph of y < 2x + 3 is a dashed line representing the equation y = 2x + 3, with the area below the line shaded.

Front

What does it mean if a line is dashed in a graph of inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set (the inequality is strict, such as '<' or '>').

Front

What does it mean if a line is solid in a graph of inequalities?

Back

A solid line indicates that points on the line are included in the solution set (the inequality is non-strict, such as '≤' or '≥').

Front

How can you tell which side of the line to shade for the inequality y > 3x - 2?

Back

To determine which side to shade, pick a test point not on the line (like (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.