Solving Systems of Equations 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, making it possible to solve for the other variable.

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What is the elimination method?

Back

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

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

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Solve the following system by elimination: 2x + 3y = 6 and 4x + 6y = 12.

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Infinitely many solutions.

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Solve the following system by elimination: 5x - 2y = 3 and 10x - 4y = 6.

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Infinitely many solutions.

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Solve the following system by elimination: 3x + 4y = 10 and 3x + 4y = 12.

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No solution.

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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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How can you make the coefficients of one variable the same in both equations?

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Multiply one or both equations by a number to achieve the same coefficient for one variable.