System of Equations - Elimination (no multiplying)

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What is a system of equations?

Back

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?

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

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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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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The equations represent parallel lines that never intersect, meaning there are no values that satisfy both equations.

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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 any point on the line is a solution.

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How do you determine if two equations are equivalent?

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If one equation can be transformed into the other by multiplying or dividing by a non-zero number.

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What is the first step in using 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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How can you eliminate a variable in a system of equations?

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By adding or subtracting the equations to cancel out one of the variables.

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What is the importance of checking your solution in a system of equations?

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To ensure that the values found satisfy all equations in the system.