Flashcard 5.3-5.4 Big Ideas Algebra I

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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 is the point(s) where the equations intersect.

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What does it mean to eliminate a variable in a system of equations?

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Eliminating a variable means manipulating the equations to remove one variable, making it easier to solve for the other variable.

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What is the elimination method?

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The elimination method involves adding or subtracting equations to eliminate one variable, allowing for easier solving of the system.

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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

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If a system has no solution, it means the lines represented by the equations are parallel and will never intersect.

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

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If a system has infinite solutions, it means the equations represent the same line, and there are countless points of intersection.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting the equations on a graph and identifying the point(s) where they intersect.

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

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Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

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How can you determine which variable to eliminate first?

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Choose the variable that can be easily eliminated with the least amount of manipulation, often based on the coefficients.

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What is the result of the equation 0 = -22?

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This indicates that there is no solution to the system, as it represents a contradiction.