Solving Systems of Linear Equations WORD PROBLEMS

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations that share the same variables. The solution to the system 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 substitution method in solving systems of equations?

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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 elimination method in solving systems of equations?

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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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How can word problems be translated into systems of equations?

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Word problems can be translated into systems of equations by identifying the variables, writing equations based on the relationships described, and ensuring the equations reflect the problem's conditions.

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What is a variable in the context of a system of equations?

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A variable is a symbol used to represent an unknown quantity in an equation, often denoted by letters such as x, y, or z.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

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What does it mean for two equations to be inconsistent?

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Two equations are inconsistent if they have no solutions, meaning their graphs are parallel and never intersect.

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What is a dependent system of equations?

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

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

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