What type of line is used for inequalities with $$\geq$$ or $$\leq$$ ?

A solid line is used for inequalities with $$\geq$$ (greater than or equal to) or $$\leq$$ (less than or equal to) because the points on the line are included in the solution.

What does the inequality $$x \geq 5$$ represent graphically?

The inequality $$x \geq 5$$ represents a vertical line at $$x = 5$$ , which is solid, and the region to the right of the line is shaded.

What does the inequality $$y \geq -3x + 4$$ indicate about the graph?

The inequality $$y \geq -3x + 4$$ indicates that the line $$y = -3x + 4$$ is solid, and the region above the line is shaded.

How do you solve a system of inequalities by graphing?

To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

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

A solid line is used for inequalities that include equality (e.g., $$\geq$$ or $$\leq$$ ), while a dotted line is used for strict inequalities (e.g., $$ $$ ).

What does the solution to the system of inequalities represent?

The solution to the system of inequalities represents all the points (x, y) that satisfy all inequalities in the system.

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

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

What is the graphical representation of the inequality $$y

The graphical representation of the inequality $$y

What does it mean if a point lies on the boundary line of an inequality?

If a point lies on the boundary line of an inequality, it is included in the solution set if the inequality is non-strict (e.g., $$\geq$$ or $$\leq$$ ) and excluded if the inequality is strict (e.g., $$ $$ ).

How do you identify the feasible region in a system of inequalities?

The feasible region in a system of inequalities is identified by shading the regions of each inequality and finding the area where all shaded regions overlap.

What is the importance of understanding systems of inequalities in real-world applications?

Understanding systems of inequalities is important in real-world applications such as optimization problems, resource allocation, and decision-making processes.

Systems of Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

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 region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

4.

FLASHCARD QUESTION

Front

Back

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CCSS.HSA.REI.D.12

5.

FLASHCARD QUESTION

Front

How do you determine the solution set for a system of inequalities?

Back

The solution set for a system of inequalities is determined by finding the overlapping region of the graphs of the individual inequalities.

Tags

CCSS.HSA.REI.D.12

6.

FLASHCARD QUESTION

Front

What is the significance of a dotted line in graphing inequalities?

Back

Tags

CCSS.HSA.REI.D.12

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

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