Systems of Equations Substitution and Elimination Methods

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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 to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system.

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What is the elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

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What is the substitution method?

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A technique for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

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

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If the equations represent parallel lines, they will never intersect, indicating no solution.

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

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The equations represent the same line, meaning every point on the line is a solution.

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What is the first step in the elimination method?

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Align the equations so that corresponding variables and constants are in the same columns.

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What is the first step in the substitution method?

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Solve one of the equations for one variable in terms of the other variable.

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How can you check your solution for a system of equations?

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Substitute the values back into the original equations to verify they hold true.

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What is a consistent system of equations?

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A system that has at least one solution.