Systems of Equations by Elimination

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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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations by elimination?

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Solving a system of equations by elimination involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the elimination method?

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The elimination method is a technique for solving systems of equations by removing one variable, allowing for the solution of the other variable.

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What does it indicate if a system of equations has an infinite number of solutions?

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An infinite number of solutions indicates that the equations represent the same line, meaning every point on the line is a solution.

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What does it mean if a system of equations has no solution?

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No solution means that the equations represent parallel lines that never intersect, indicating that there are no common solutions.

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How do you determine if two equations are dependent?

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Two equations are dependent if they represent the same line, which can be determined if one equation can be obtained by multiplying the other by a non-zero constant.

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What is the first step in using the elimination method?

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The first step is to align the equations and manipulate them (by multiplication or addition) to create coefficients for one variable that are opposites.

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

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You can check your 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 whether they intersect, are parallel, or are the same line.

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What is a consistent system of equations?

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A consistent system has at least one solution, which can be either a single point of intersection or infinitely many solutions.