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 ordered pairs 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be 'not a solution' to a system of inequalities?

Back

A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the half-plane indicates the region where the inequality holds true.

Front

What is the difference between a solid line and a dashed line in the graph of an inequality?

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 graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, shading the appropriate region for each. The solution set is where the shaded regions overlap.

Front

What does the inequality x > -3 represent graphically?

Back

The inequality x > -3 represents all points to the right of the vertical line x = -3, not including the line itself.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is solid or dashed. Then, assess which side of the line is shaded to determine the inequality direction.

Front

What does the ordered pair (-3, 0) represent in the context of a system of inequalities?

Back

The ordered pair (-3, 0) represents a specific point in the coordinate plane that can be tested to see if it satisfies the inequalities in the system.