Solving 3-variable systems REVIEW

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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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions when the equations represent the same line or plane, meaning there are countless points that satisfy all equations.

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What is the elimination method in solving systems of equations?

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

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equations.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines or planes that never intersect.

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What is the geometric interpretation of a system of three equations in three variables?

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The geometric interpretation involves visualizing the equations as planes in three-dimensional space, where the solution is the point of intersection of the planes.

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What is a unique solution in the context of systems of equations?

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A unique solution occurs when the equations intersect at exactly one point, meaning there is one set of values that satisfies all equations.

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

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You can check your solution by substituting 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, affecting the nature of the solutions.

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What is a dependent system of equations?

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A dependent system is one where the equations are not independent, meaning one equation can be derived from another, leading to infinitely many solutions.