Solving Systems of Equations with Elimination REVISED

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 eliminate a variable in a system of equations?

Back

To remove one variable from the equations, making it easier to solve for the other variable.

Front

What is the elimination method?

Back

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

Front

When is it possible to eliminate a variable without changing the equations?

Back

When the coefficients of one variable are already opposites or can be made opposites by multiplying.

Front

What does it indicate if you end up with a statement like 0=2 when solving a system?

Back

It indicates that there is no solution to the system of equations.

Front

What is the first step in the elimination method?

Back

Identify which variable to eliminate and manipulate the equations accordingly.

Front

How can you make the coefficients of a variable opposites?

Back

By multiplying one or both equations by a suitable number.

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What is the significance of having infinite solutions in a system of equations?

Back

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

Front

What does it mean if a system of equations has exactly one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

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What is a coefficient in an equation?

Back

A numerical factor that multiplies a variable in an equation.