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 point(s) where the equations intersect.

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What are the three main methods for solving systems of equations?

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

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When is substitution the best method to solve a system of equations?

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Substitution is best when one equation is easily solvable for one variable, allowing for straightforward substitution into the other equation.

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What does it mean to graph a system of equations?

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Graphing a system of equations involves plotting each equation on the same coordinate plane to visually identify the point(s) of intersection, which represent the solution.

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

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To use elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

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What is the solution to a system of equations?

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The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

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What is the significance of the point of intersection in a graph of two lines?

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The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.

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How can you check if a solution to a system of equations is correct?

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You can check a solution by substituting the values back into the original equations to see if they hold true.

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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 other variable.

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.