Solving 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.

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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 elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

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How do you eliminate a variable in a system of equations?

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By manipulating the equations (e.g., multiplying, adding) to cancel out one variable.

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What is the substitution method?

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A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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

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The lines represented by the equations are parallel and never intersect.

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

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The equations represent the same line, meaning every point on the line is a solution.

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How can you tell if a system of equations is ready for elimination?

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If the coefficients of one variable are opposites or can be made opposites through multiplication.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.