Choose a Method - 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 to solve systems of equations?

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1. Graphing 2. Substitution 3. Elimination

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When is the substitution method most efficient?

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The substitution method is most efficient when one equation is easily solvable for one variable.

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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.

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When is the elimination method preferred?

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The elimination method is preferred when the coefficients of one variable are the same or can be easily manipulated to be the same.

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What does it mean to graph a system of equations?

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Graphing a system of equations means plotting both equations on the same coordinate plane to find their intersection point(s), which represents the solution.

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What is the graphical method of solving systems of equations?

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The graphical method involves drawing the lines represented by the equations and identifying their intersection point.

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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 lines intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.