Solving systems of equations by elimination

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What is the elimination method in solving systems of equations?

Back

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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What does it mean if a system of equations has one solution?

Back

It means the two lines intersect at exactly one point, representing a unique solution for the variables.

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

Back

It means the two lines are parallel and will never intersect, indicating that there is no set of values for the variables that satisfies both equations.

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What does it mean if a system of equations has infinite solutions?

Back

It means the two lines are identical (overlapping), and every point on the line is a solution to the system.

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How do you determine if two equations are independent?

Back

Two equations are independent if they represent two lines that intersect at exactly one point.

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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, resulting in infinite solutions.

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What is the first step in using the elimination method?

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The first step is to manipulate the equations to align coefficients of one variable so that they can be eliminated.

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3,0) is the solution.

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Solve by elimination: 5x + 2y = 10 and 5x - 2y = 0.

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(2,0) is the solution.

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What is the result of adding two equations in a system?

Back

The result is a new equation that combines the information from both equations, which can help in finding the solution.