2.3 and 2.4 System of Equation

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What is a system of equations?

Back

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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What is a solution to a system of inequalities?

Back

A solution to a system of inequalities is any ordered pair that satisfies all inequalities in the system.

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How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, using dashed lines for '<' or '>' and solid lines for '≤' or '≥'. The solution is the overlapping shaded region.

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What does it mean if a point is a solution to a system of inequalities?

Back

If a point is a solution to a system of inequalities, it means that the point satisfies all the inequalities in the system.

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

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A solution to a system of equations is a specific point where the equations intersect, while a solution to a system of inequalities is a range of points that satisfy the inequalities.

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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, where one side of the line represents the solutions.

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

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The feasible region is the area on a graph where all the solutions to a system of inequalities exist.

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How can 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 it satisfies all inequalities, it is a solution.

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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 all equations are satisfied simultaneously.

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What is a linear inequality?

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A linear inequality is an inequality that involves a linear expression, typically written in the form ax + by < c, ax + by > c, etc.