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 that are solved simultaneously.

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

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It means that the equations represent the same line or plane, and any point on that line or plane is a solution.

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

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If the equations represent parallel lines that never intersect, the system has no solution.

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What is the graphical representation of a system of equations?

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The solutions to a system of equations can be represented as the points of intersection of the graphs of the equations.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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How do you solve a system of equations using the graphing method?

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By graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What is the significance of the coefficients in a system of equations?

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Coefficients determine the slope and position of the lines represented by the equations.

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What does it mean for two equations to be dependent?

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

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What does it mean for two equations to be independent?

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Independent equations are those that represent different lines, resulting in either one solution or no solution.