Solving Systems by Elimination

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What is a system of equations?

Back

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 by elimination?

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It means to eliminate one variable by adding or subtracting the equations to find the value of the other variable.

Front

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

Back

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

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How do you eliminate a variable in a system of equations?

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You can multiply one or both equations by a number to make the coefficients of one variable opposites, then add or subtract the equations.

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What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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What is the elimination method?

Back

A method for solving systems of equations by removing one variable to solve for the other.

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When is a system of equations considered inconsistent?

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When there is no solution, meaning the lines are parallel and never intersect.

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

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It means the equations represent the same line, and every point on that line is a solution.

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

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By substituting the solution back into the original equations to see if both equations are satisfied.

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What is a coefficient in an equation?

Back

A numerical factor that multiplies a variable in an equation.