System of Equations Word Problems

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Define a system of equations.

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the point(s) where the graphs of the equations intersect. Each intersection point represents a solution to the system.

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How do you solve a system of equations using substitution?

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To solve a system using substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Front

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.

Front

Write a system of equations based on a word problem involving costs.

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Identify the variables, set up equations based on the relationships described in the problem, and ensure the equations reflect the total costs or quantities involved.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations 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 of equations 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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To check the solution, substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Front

What is the importance of defining variables in word problems?

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Defining variables clearly helps to translate the problem into mathematical equations, making it easier to set up and solve the system.