Systems of Equations Mastery Flashcard

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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 for a system of equations to have exactly one solution?

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It means the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

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It means the graphs of the equations are parallel and never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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It means the graphs of the equations overlap completely, representing the same line.

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How can you determine if a system of equations has one solution, no solution, or infinitely many solutions by looking at their graphs?

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One solution: intersecting lines; No solution: parallel lines; Infinitely many solutions: overlapping lines.

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What is the substitution method for 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 for solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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Write a system of equations for the following scenario: A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys 10 items and spends $5.00, what are the equations?

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What is the graphical representation of the solution to a system of equations?

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The point(s) where the graphs of the equations intersect.