Mastering Linear Systems and Inequalities

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What is a linear system?

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A linear system is a collection of one or more linear equations involving the same variables.

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What does it mean for a point to be a solution to a linear system?

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A point is a solution to a linear system if it satisfies all the equations in the system.

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What is the elimination method in solving linear systems?

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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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How do you determine if a point is a solution to a system of equations?

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Substitute the coordinates of the point into each equation. If the equations hold true, the point is a solution.

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What is the graphical representation of a linear equation?

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A linear equation can be represented graphically as a straight line on a coordinate plane.

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What is the intersection of two lines in a graph?

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The intersection of two lines represents the solution to the system of equations, where both equations are satisfied.

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What is a consistent system of equations?

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

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

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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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