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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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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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 other variable.

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

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A consistent system 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 has no solutions, meaning the equations do not intersect at any point.

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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 represent a system of equations graphically?

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You can graph each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) of the system.

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

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Identify the variables and what they represent in the context of the problem.

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How do you translate a word problem into a system of equations?

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Break down the problem into mathematical statements based on the relationships described in the text.

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What is the importance of checking your solution in a system of equations?

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Checking your solution ensures that it satisfies all equations in the system, confirming its validity.