Writing 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 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 is a technique for solving systems of equations by adding or subtracting equations to eliminate one 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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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What is the first step in using the Elimination Method?

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The first step is to align the equations and decide which variable to eliminate by manipulating the equations.

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What does it mean to have a unique solution in a system of equations?

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A unique solution means there is exactly one set of values for the variables that satisfies all equations in the system.

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What is an inconsistent system of equations?

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An inconsistent system is one that has no solution, meaning the equations represent parallel lines that 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.

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How can you check the solution of a system of equations?

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