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.

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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 does the symbol '≤' mean 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 '>' mean 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.

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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 is solid if the inequality includes equality (≤ or ≥) and dashed if it does not (< or >).

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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 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.

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What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it may or may not be a solution depending on whether the inequality includes equality (≤ or ≥).

Front

What is the difference between 'solution' and 'not a solution' in the context of inequalities?

Back

'Solution' means the point satisfies all inequalities in the system, while 'not a solution' means it does not satisfy at least one inequality.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection of two inequalities, graph both inequalities and identify the region where their shaded areas overlap.