System of Equations (elimination)

Front

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?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

Front

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

Back

The equations represent the same line, meaning there are countless points that satisfy both equations.

Front

What does it mean if a system of equations has no solutions?

Back

The equations represent parallel lines that never intersect, indicating there are no common solutions.

Front

Solve the system of equations: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite solutions.

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Solve the system of equations: x + y = 5 and x - y = 1.

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(3, 2).

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

How can you manipulate equations to use the elimination method?

Back

You can multiply one or both equations by a constant to create coefficients that will cancel out one variable when added or subtracted.

Front

Solve the system of equations: 3x + 4y = 10 and 6x + 8y = 20.

Back

Infinite solutions.