Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations that have the same variables.

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

Back

It means that there are an infinite number of ordered pairs that satisfy all equations in the system.

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What is the solution of a system?

Back

The ordered pair that satisfies all equations in the system.

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What does the graph of a system with no solution look like?

Back

The graph consists of parallel lines.

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What is one solution in a system of equations?

Back

It is a unique ordered pair that satisfies all equations in the system.

Front

What is the elimination method?

Back

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

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What is a consistent system of equations?

Back

A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What does it mean for two lines to be intersecting in a graph of a system of equations?

Back

It means that the system has exactly one solution, represented by the point of intersection.

Front

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

Back

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