A1P1 Systems of Inequalities Review

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 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 it mean for a point to be a solution in the context of inequalities?

Back

A point is a solution if it lies in the region defined by the inequalities, meaning it satisfies all the conditions set by the inequalities.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to a specified number.

Front

How do you graph the inequality x < -1?

Back

To graph x < -1, draw a vertical dashed line at x = -1 and shade the region to the left of the line, indicating all values less than -1.

Front

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

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

What is the solution set of the inequality y > 2?

Back

The solution set includes all points above the horizontal line y = 2, not including the line itself.

Front

How can you check if a point is a solution to the inequality y ≤ 3?

Back

Substitute the y-coordinate of the point into the inequality. If the y-coordinate is less than or equal to 3, then the point is a solution.