2.3 and 2.4 System of Equation

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a solution to a system of inequalities?

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A solution to a system of inequalities is a set of values that satisfy all inequalities in the system, often represented as a region on a 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 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 '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.

Tags

CCSS.HSA.REI.D.12

Front

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 difference between a system of equations and a system of inequalities?

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A system of equations has exact solutions (points of intersection), while a system of inequalities has a range of solutions (regions) that satisfy the inequalities.

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CCSS.HSA.REI.C.7

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What is the first step in solving a system of inequalities by graphing?

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The first step is to graph each inequality on the same coordinate plane, using dashed lines for '<' or '>' and solid lines for '≤' or '≥'.

Tags

CCSS.HSA.REI.D.12

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What does the term 'feasible region' refer to in the context of inequalities?

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

Tags

CCSS.HSA.REI.D.12

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How can you check if a point lies within the feasible region?

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Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it lies within the feasible region.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the intersection point in a system of equations?

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The intersection point represents the solution to the system, where both equations are satisfied simultaneously.

Tags

CCSS.8.EE.C.8A