4-7 Day 2 Practice

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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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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 does it mean for a point to be NOT a solution to a system of inequalities?

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A point is NOT a solution if it does not satisfy at least one of the inequalities in the system.

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Tags

CCSS.HSA.REI.D.12

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

Back

The boundary line represents the points where the inequality changes from true to false. It is included in the solution if the inequality is 'less than or equal to' or 'greater than or equal to'.

Tags

CCSS.HSA.REI.D.12

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between 'greater than' and 'greater than or equal to' in inequalities?

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'Greater than' (>) means the boundary is not included, while 'greater than or equal to' (≥) means the boundary is included in the solution set.

Tags

CCSS.6.EE.B.8

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How do you solve a system of equations graphically?

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To solve graphically, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. These points are the solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a feasible region in the context of linear inequalities?

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

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6