Solving Systems using Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variable.

Front

How do you determine if a system of equations has a unique solution, no solution, or infinitely many solutions?

Back

A system has a unique solution if the lines intersect at one point, no solution if the lines are parallel, and infinitely many solutions if the lines coincide.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (by multiplication or addition) to eliminate one of the variables.

Front

How can you manipulate equations to prepare for elimination?

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You can multiply one or both equations by a constant to make the coefficients of one variable opposites.

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What does it mean if two equations in a system are dependent?

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Dependent equations are those that represent the same line, resulting in infinitely many solutions.

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What does it mean if two equations in a system are independent?

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Independent equations are those that represent different lines, resulting in a unique solution.

Front

What is the significance of the coefficients in the elimination method?

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The coefficients determine how the equations can be manipulated to eliminate a variable; they must be adjusted to be opposites for effective elimination.

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How do you check your solution after solving 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 result of the elimination method if the two equations are identical?

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If the two equations are identical, the result is an infinite number of solutions.

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What is the result of the elimination method if the two equations are contradictory?

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If the two equations are contradictory (e.g., parallel lines), the result is no solution.