Systems - Number of Solutions (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.

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What does it mean if a system of equations has one solution?

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The lines representing the equations intersect at exactly one point.

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

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The lines representing the equations are parallel and never intersect.

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

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The lines representing the equations coincide, meaning they are the same line.

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How can you determine the number of solutions in a system of equations?

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By graphing the equations or using substitution or elimination methods.

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

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Two lines intersecting at a single point.

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What is the graphical representation of a system with no solution?

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Two parallel lines that never meet.

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What is the graphical representation of a system with infinite solutions?

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Two lines that lie on top of each other.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable.