Systems of Linear Inequalities

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What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve the same variables. The solution set is the region where the graphs of the inequalities overlap.

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

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 side is either smaller than or equal to the value on the right side.

Front

When graphing an inequality, what type of line is used for '>' or '<'?

Back

A dotted line is used when graphing inequalities with '>' or '<' to indicate that the points on the line are not included in the solution set.

Front

When graphing an inequality, what type of line is used for '≥' or '≤'?

Back

A solid line is used when graphing inequalities with '≥' or '≤' to indicate that the points on the line are included in the solution set.

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How do you determine if a point is part of the solution set for a system of inequalities?

Back

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

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

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What is the solution set of a system of linear inequalities?

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