Solve Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by combining equations to eliminate one variable.

Front

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

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

Back

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

Front

What is the first step in the elimination method?

Back

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

Front

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

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Infinite Solutions.

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

Back

(4, 0).

Front

What is the result of adding two equations in a system?

Back

You can eliminate one variable, making it easier to solve for the other.

Front

Solve the system by elimination: x + 2y = 10 and 2x + 4y = 20.

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Infinite Solutions.