Systems of Three Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean for a system of equations to have a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

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It means that there are no values for the variables that can satisfy all equations simultaneously.

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What does it mean for a system of equations to have infinitely many solutions?

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It means that there are an infinite number of values for the variables that satisfy all equations in the system.

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How do you solve a system of three equations?

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You can use methods such as substitution, elimination, or matrix operations to find the values of the variables.

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What is the elimination method?

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

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What is the substitution method?

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A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equations.

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What is a consistent system of equations?

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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 is a dependent system of equations?

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