Systems of Equations Elimination

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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 to solve a system of equations by elimination?

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It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is a solution to a system of equations?

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A set of values for the variables that makes all equations in the system true.

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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 an infinite number of 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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How do you determine if a system of equations has no solution?

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If the equations are inconsistent, meaning they represent parallel lines.

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How do you determine if a system of equations has an infinite number of solutions?

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If the equations are dependent, meaning they represent the same line.

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

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Align the equations so that like terms are in the same column.

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What is the purpose of multiplying an equation in a system?

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To create coefficients that allow for easy elimination of a variable.