A1-5.4 FLASHCARD Systems by Elimination

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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 with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the elimination method?

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The elimination method is a technique used to solve systems of equations by removing one variable, allowing for easier calculation of the other variable.

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How do you determine which variable to eliminate in a system of equations?

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Look for coefficients that can easily be made equal or opposite through multiplication, allowing for straightforward addition or subtraction.

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What is the first step in solving a system of equations by elimination?

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The first step is to align the equations and manipulate them, if necessary, to make the coefficients of one variable equal.

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(2, 3)

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the lines represented by the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the lines represented by the equations are parallel and never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

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Infinitely many solutions (dependent system).