Systems of Equations Applications

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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 set of values that satisfy all equations in the system.

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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 make all equations true simultaneously.

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What are the three possible outcomes when solving a system of equations?

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1. One unique solution (intersecting lines), 2. No solution (parallel lines), 3. Infinitely many solutions (coincident lines).

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How do you represent a system of equations algebraically?

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for 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 check the solution of a system of equations?

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You can check the solution by substituting the values of the variables back into the original equations to see if they hold true.

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What is a consistent system of equations?

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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 is an inconsistent system of equations?

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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 does it mean if a system of equations has infinitely many solutions?

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If a system has infinitely many solutions, it means that the equations represent the same line, and there are countless points that satisfy both equations.