Systems of Inequalities

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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 points that satisfy all inequalities in the system.

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 the inequalities in the system, meaning it lies in the shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

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How do 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the difference between a system of equations and a system of inequalities?

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Systems of equations have specific solutions (one, none, or infinitely many), while systems of inequalities can have a range of solutions represented by a shaded region.

Tags

CCSS.HSA.REI.C.7

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of the shaded regions that satisfy the inequalities, often bounded by lines that represent the equations of the inequalities.

Tags

CCSS.HSA.REI.D.12

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What does the shaded region in a graph of inequalities represent?

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The shaded region represents all the possible solutions that satisfy the inequalities in the system.

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 equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region.

Tags

CCSS.HSA.REI.D.12

Front

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

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The boundary line separates the solutions from the non-solutions. Points on the line are included if the inequality is ≤ or ≥.

Tags

CCSS.HSA.REI.D.12

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What is an example of a system of inequalities?

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Example: y < 2x + 3 and y ≥ -x - 1. This system includes all points that satisfy both inequalities.

Tags

CCSS.HSA.REI.D.12

Front

How can you solve a system of inequalities by graphing?

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To solve by graphing, graph each inequality on the same coordinate plane, identify the shaded regions, and find the intersection of these regions.

Tags

CCSS.HSA.REI.D.12