system of equations

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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 are the methods to solve a system of equations?

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The main methods to solve a system of equations include graphing, substitution, and elimination.

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What does it mean for a system of equations to be consistent?

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

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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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 or curves represented by the equations on a coordinate plane.

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What is the substitution method for 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 equation.

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What is the elimination method for 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 variable.

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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 system of equations has exactly one solution point where the lines intersect.

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What are dependent equations in a system of equations?

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Dependent equations are equations that represent the same line, resulting in infinitely many solutions.

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What are independent equations in a system of equations?

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Independent equations are equations that represent different lines, resulting in a unique solution.