Systems of Equations

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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 that have the same variables.

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

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It means the lines represented by 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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It means the lines represented by the equations are parallel and never intersect.

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

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It means the lines represented by the equations overlap completely.

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What do parallel lines represent in a system of equations?

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Parallel lines represent a system of equations with no solution.

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What do intersecting lines represent in a system of equations?

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Intersecting lines represent a system of equations with one unique solution.

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What do overlapping lines represent in a system of equations?

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Overlapping lines represent a system of equations with infinitely many solutions.

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How can you determine the solution of a system of equations graphically?

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By finding the point where the lines intersect on the graph.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for a variable and substituting that value into the other equation.