Systems of equations by elimination

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What is a system of equations?

Back

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 simultaneously.

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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 remaining variable.

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How do you eliminate a variable in a system of equations?

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To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

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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 represent parallel lines that never intersect.

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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 intersection points of the lines represented by the equations on a coordinate plane.

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What is the first step in solving a system of equations by elimination?

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The first step is to align the equations and decide which variable to eliminate.

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How can you check if your solution to a system of equations is correct?

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

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What is the significance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting their intersection and the nature of the solution.

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What happens if the coefficients of the variables are the same in both equations?

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If the coefficients are the same and the constants are different, the system is inconsistent (parallel lines). If both coefficients and constants are the same, the system has infinitely many solutions (the same line).