Systems of Equations Flashcard - All Methods

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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 is the point(s) where the equations intersect.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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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 equation.

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

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

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values back into the original equations to see if they hold true.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection points of the lines represented by the equations on a coordinate plane.

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What is the first step in solving a system of equations by substitution?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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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, affecting their intersection.

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How can you identify a system of equations that has a unique solution?

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A system has a unique solution if the lines intersect at exactly one point, meaning the equations are not parallel or identical.