Solutions to Systems of Inequalities- Graphs!

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Then, determine the solution region by shading the area that satisfies all inequalities.

Tags

CCSS.HSA.REI.D.12

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What does it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system when the coordinates of the point are substituted into the inequalities.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

Tags

CCSS.6.EE.B.8

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What is the solution region in a graph of inequalities?

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The solution region is the area on the graph where all the inequalities in the system overlap, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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How do you determine if a point is in the solution region?

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To determine if a point is in the solution region, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is in the solution region.

Tags

CCSS.HSA.REI.D.12

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What does the term 'ordered pair' mean?

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An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y).

Tags

CCSS.5.G.A.1

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What is the significance of the boundary line in a graph of inequalities?

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The boundary line represents the points where the inequality changes from true to false. For strict inequalities, the line is dashed; for non-strict inequalities, it is solid.

Tags

CCSS.HSA.REI.D.12

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How can you tell if a point is a solution to a specific inequality?

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Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

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What does it mean if a solution is 'not a solution' to a system of inequalities?

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If a point is 'not a solution,' it means that when the coordinates are substituted into the inequalities, at least one inequality is not satisfied.

Tags

CCSS.HSA.REI.D.12