System of Equations (elimination)

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What is a system of equations?

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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 to solve a system of equations using elimination?

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Solving a system of equations using elimination involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the elimination method?

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The elimination method is a technique for solving systems of equations by eliminating one variable, allowing the other variable to be solved directly.

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

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A system of equations has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations. The intersection point(s) represent the solution(s) to the system.

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

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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 first step in using the elimination method?

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The first step in using the elimination method is to align the equations and manipulate them (by multiplying if necessary) so that the coefficients of one variable are opposites.

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What is a consistent system of equations?

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A consistent system of equations is one that has at least one solution, which can be either a unique solution or infinitely many solutions.

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What is an inconsistent system of equations?

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An inconsistent system of equations is one that has no solutions, typically represented by parallel lines.