Systems of Equations - Which Method is Best?

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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 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 satisfy all equations in the system simultaneously.

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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 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 equal values method?

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The equal values method involves setting two expressions equal to each other when both represent the same variable, allowing for easier solving.

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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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When is the substitution method preferred?

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The substitution method is preferred when one equation is already solved for one variable or can be easily rearranged.

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When is the equal values method preferred?

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The equal values method is preferred when both equations are already solved for the same variable.

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What is a consistent system of equations?

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A consistent system of equations 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 of equations has no solution, meaning the lines are parallel and never intersect.