Solving Systems of Linear Inequalities

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What is a system of linear inequalities?

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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.

Tags

CCSS.HSA.REI.D.12

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How do you graph a linear inequality?

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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.

Tags

CCSS.HSA.REI.D.12

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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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.6.EE.B.8

Front

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

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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 '≤').

Tags

CCSS.HSA.REI.D.12

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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.

Tags

CCSS.8.EE.C.8B

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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?

Back

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

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12