System of Inequalities: Solution or Not a Solution?

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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.

Tags

CCSS.HSA.REI.D.12

Front

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.

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What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

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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 half-plane divided by a line. The line is solid if the inequality is inclusive (≥ or ≤) and dashed if it is exclusive (> or <).

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12

Front

How do you graph the inequality y ≤ -2x + 5?

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To graph y ≤ -2x + 5, first graph the line y = -2x + 5 as a solid line. Then shade below the line to represent all points where y is less than or equal to -2x + 5.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution set of a system of inequalities look like?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, which is the solution to the system.

Tags

CCSS.HSA.REI.D.12

Front

How can you check if a point is not a solution to a system of inequalities?

Back

To check if a point is not a solution, substitute the point's coordinates into the inequalities. If it fails to satisfy any inequality, it is not a solution.

Front

What is the meaning of the term 'feasible region' in the context of inequalities?

Back

The feasible region is the area on a graph that represents all possible solutions to a system of inequalities.

Tags

CCSS.HSA.REI.D.12