Solving Systems with Three Variables

Front

What is a system of linear equations?

Back

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

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so there are countless points of intersection.

Front

How do you determine if a system of equations has a unique solution?

Back

A unique solution exists if the equations represent lines that intersect at exactly one point.

Front

What is the graphical representation of a system of three linear equations?

Back

It can be represented as three planes in three-dimensional space.

Front

What is the method of substitution in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equations.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the others.

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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?

Back

A system that has no solutions.

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What is a dependent system of equations?

Back

A system where the equations represent the same line, resulting in infinitely many solutions.