Solving 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 word problems be translated into equations?

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Identify the variables, write equations based on the relationships described in the problem, and use the information given to form a system of equations.

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What is the importance of defining variables in word problems?

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Defining variables helps clarify what each variable represents, making it easier to set up equations and understand the problem.

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What is a linear equation?

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How do you interpret the solution of a system of equations graphically?

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The solution of a system of equations is the point(s) where the graphs of the equations intersect. This point represents the values of the variables that satisfy all equations.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system of equations has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.