Systems of Equations Word Problems

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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 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 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 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 they 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 they 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.

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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and intercepts of the equations: if they are the same, there are infinitely many solutions; if they are different, there is one solution; if they are parallel, there are no solutions.

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What is the first step in solving a word problem involving a system of equations?

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The first step is to define the variables that represent the unknown quantities in the problem.