5.4 Solving Special Systems of Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean if a system of equations has no solution?

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It means that the equations represent parallel lines that never intersect.

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What does it mean if a system of equations has infinite solutions?

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It means that the equations represent the same line, so every point on the line is a solution.

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What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

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How can you determine if two equations are equivalent?

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If you can manipulate one equation to become the other through algebraic operations.

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Back

No Solution (the lines are parallel).

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Back

One Solution: (1, 4).

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What does the term 'intersecting lines' refer to in the context of systems of equations?

Back

Lines that cross each other at one point, indicating a unique solution.

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

Back

It represents the solution to the system, where both equations are satisfied.

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Infinite Solutions (the same line).