System 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 determine if a point is a solution to a system of inequalities?

Back

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

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How do you graph the inequality y < -x + 2?

Back

To graph y < -x + 2, first graph the line y = -x + 2 as a dashed line. Then shade the area below the line to represent all points where y is less than -x + 2.

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where the shaded areas of all inequalities overlap.

Front

How can you check if a point lies in the solution set of a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it lies in the solution set.

Front

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

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Front

What is the graphical representation of the inequality y ≥ x + 4?

Back

The graphical representation of y ≥ x + 4 is a solid line for y = x + 4, with the area above the line shaded to indicate all points where y is greater than or equal to x + 4.