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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations in the system true at the same time.

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What are the three methods for solving systems of equations?

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The three methods are: 1) Graphing, 2) Substitution, 3) Elimination.

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What is the substitution method?

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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?

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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 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 can you determine if a system of equations is consistent or inconsistent?

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A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

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What is the graphical representation of a system of equations?

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The graphical representation involves plotting each equation on a coordinate plane and identifying the point(s) of intersection.

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

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