Systems of Linear Equations

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What is a system of linear equations?

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A system of linear equations is two or more linear equations that share the same variables.

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

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A consistent and independent system has exactly one solution, where the lines representing the equations intersect at a single point.

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What is an inconsistent system of equations?

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An inconsistent system is a system of equations that has no solution, meaning the lines are parallel and never intersect.

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What is the graphical method for solving a system of linear equations?

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The graphical method involves plotting the equations on a graph and identifying the point(s) where they intersect.

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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 other variable.

Front

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

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A consistent system has at least one solution, which can be either one solution (independent) or infinitely many solutions (dependent).

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What is a dependent system of equations?

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A dependent system is a system of equations that has infinitely many solutions, meaning the equations represent the same line.

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How can you determine if two equations are independent?

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Two equations are independent if their graphs intersect at exactly one point, indicating a unique solution.

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What is the importance of the slope in linear equations?

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The slope indicates the steepness of the line and the direction of the relationship between the variables in the equation.