Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

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

Back

'>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

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

Back

'<'' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

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

Back

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

Front

What is a solution to a system of inequalities?

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A solution to a system of inequalities is an ordered pair (x, y) that satisfies all inequalities in the system.

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How can you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the x and y values into each inequality. If the point satisfies all inequalities, it is a solution.

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What does it mean if a point lies in the shaded region of a graph of inequalities?

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If a point lies in the shaded region, it means that the point satisfies the inequalities represented by the graph.

Front

What is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of solutions that satisfy both inequalities simultaneously.

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How do you find the boundary line of a linear inequality?

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To find the boundary line, convert the inequality to an equation by replacing the inequality sign with an equal sign and graph that line.