Classifying Systems 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 is the set of values that satisfy all equations simultaneously.

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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 remaining variable.

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What is the graphical method of solving a system of equations?

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The graphical method involves plotting each equation on a graph and identifying the point(s) where the lines intersect, which represents the solution(s) to the system.

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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 represent a system of equations algebraically?

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A system of equations can be represented in the form: 1. Ax + By = C 2. Dx + Ey = F, where A, B, C, D, E, and F are constants.

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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 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 the number of solutions.

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

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The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

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What is a consistent system of equations?

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A consistent system has at least one solution, which can be either one unique solution or infinitely many solutions.