Solving Systems of Equations with 3 variables

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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.

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

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

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What is the graphical representation of a system of equations with one solution?

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Two lines that intersect at a single point.

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

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable.

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What does it mean for a system of equations to be consistent?

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A system is consistent if it has at least one solution.

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What does it mean for a system of equations to be inconsistent?

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A system is inconsistent if it has no solutions.

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How can you determine if a system of equations has infinitely many solutions?

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If the equations represent the same line, they have infinitely many solutions.

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What is a 3-variable system of equations?

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A system that consists of three equations with three variables, typically represented as x, y, and z.

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What is the role of the determinant in solving systems of equations?

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The determinant helps determine if a unique solution exists for a system of linear equations.