Solving Systems with 3 Variables

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What is a system of equations with 3 variables?

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A set of equations that have three different variables, which can be solved simultaneously to find the values of those variables.

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What does it mean to solve a system of equations?

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To find the values of the variables that satisfy all equations in the system at the same time.

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What is an ordered triple?

Back

A set of three elements in a specific order, typically representing the values of three variables in a solution.

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How do you represent the solution of a system of equations with 3 variables?

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The solution is represented as an ordered triple (x, y, z), where x, y, and z are the values of the variables.

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What is the first step in solving a system of equations with 3 variables?

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Choose one equation and solve for one variable in terms of the others.

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

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Substitution is a method where you solve one equation for a variable and then substitute that expression into the other equations.

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

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the others.

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

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It means that the equations represent parallel planes that do not intersect at any point.

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

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It means that the equations represent the same plane or coincide in some way, leading to multiple intersection points.

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How can you check if your solution to a system of equations is correct?

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Substitute the values of the variables back into the original equations to see if they hold true.