Solving 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 substitution in the context of solving systems of equations?

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Substitution is 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 graphical interpretation of a system of equations?

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The solutions to a system of equations can be represented graphically as the points where the lines of the equations intersect.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions.

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

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

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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 to eliminate one variable, often by multiplying one or both equations.

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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.