Solving Systems of Equations with 3 variables

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What is a system of equations?

Back

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

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical representation of a system of equations?

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The intersection points of the graphs of the equations represent the solutions.

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What is a solution to a system of equations with three variables?

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A set of values (x, y, z) that satisfies all equations in the system.

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What is the substitution method 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 equations.

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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, 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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The equations represent parallel planes that do not intersect.

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

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The equations represent the same plane, leading to an infinite number of intersection points.

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How do you determine if a solution is correct for a system of equations?

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

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What is the role of coefficients in a system of equations?

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Coefficients determine the slope and position of the lines or planes represented by the equations.