A2.3A 3 Variable Systems of 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 simultaneously.

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What does it mean to solve a system of equations?

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

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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 does it mean if two equations in a system are identical?

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The system has infinite solutions because every point on the line is a solution.

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What is a unique solution in a system of equations?

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A single point where the graphs of the equations intersect.

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

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The graphs of the equations are parallel and never intersect.

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

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If the equations are equivalent, they represent the same line.

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What is the substitution method for solving systems of equations?

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Solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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Adding or subtracting equations to eliminate one variable, making it easier to solve for the others.

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What is a three-variable system of equations?

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