Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share 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. Use a dashed line for inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ or ≥). Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

Front

What does the symbol '>' represent in inequalities?

Back

'>' means that the value on the left is greater than the value on the right, not including the value on the right.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means that the value on the left is greater than or equal to the value on the right, including the value on the right.

Front

What is the solution to a system of inequalities?

Back

The solution to a system of inequalities is the set of all ordered pairs (x, y) that satisfy all inequalities in the system.

Front

What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if there is no ordered pair (x, y) that satisfies all inequalities in the system, often indicated by the shaded regions not overlapping.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Front

What does the graph of 'y > 3' look like?

Back

The graph of 'y > 3' is a horizontal dashed line at y = 3, with the region above the line shaded.

Front

How do you match inequalities to their corresponding graphs?

Back

To match inequalities to graphs, identify the boundary line (solid or dashed) and the shaded region. The direction of the shading indicates whether the inequality is greater than or less than.