Algebra 1 5.3-5.4 Flashcard

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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 no solution?

Back

A system has no solution if the lines represented by the equations are parallel and never intersect.

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes and intercepts of the lines represented by the equations.

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Back

Infinite solutions.

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Back

(3, 2).

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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.

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What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines corresponding to the equations.

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What does it mean if two equations are dependent?

Back

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

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What does it mean if two equations are independent?

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Independent equations are those that represent different lines, resulting in either one solution or no solution.