Solving 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

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

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

Front

How do you graph the inequality y < 2x + 3?

Back

To graph y < 2x + 3, draw a dashed line for y = 2x + 3 and shade below the line, indicating that all points below the line are solutions.

Front

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

Back

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

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 solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It includes all points that satisfy all inequalities.

Front

What does the inequality y > -x + 2 represent graphically?

Back

The inequality y > -x + 2 represents a region above the line y = -x + 2, where points above the line are solutions.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution set.

Front

How can you check if a point (3, 4) is a solution to the system y ≤ 2x - 1 and y > -2x + 3?

Back

Substitute (3, 4) into both inequalities: For y ≤ 2x - 1: 4 ≤ 2(3) - 1 (True). For y > -2x + 3: 4 > -2(3) + 3 (True). Thus, (3, 4) is a solution.