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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

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

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Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

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What is a three-variable system?

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A three-variable system consists of three equations with three unknowns, typically represented as x, y, and z.

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How do you represent a solution to a three-variable system?

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A solution to a three-variable system is represented as an ordered triplet (x, y, z), indicating the values of the three variables.

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

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Infinitely many solutions occur when the equations represent the same plane or line in three-dimensional space, meaning they overlap completely.

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What is the elimination method used for?

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The elimination method is used to simplify a system of equations to find the values of the variables by eliminating one variable at a time.

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.

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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.