Course3: Flashcard:5.2 Review (Systems of Equations)

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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 that have the same variables.

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What is the solution of a system?

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The ordered pair that satisfies all equations in the system.

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What is the best first step in solving the system: y = 4x + 7 and y = x - 3?

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Set the equations equal to each other: 4x + 7 = x - 3.

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What does it mean to replace a variable in an equation?

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To substitute a variable with an expression or value from another equation.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

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How do you find the intersection of two lines represented by equations?

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By solving the system of equations to find the ordered pair (x, y) that satisfies both equations.

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What is the graphical representation of a system of equations?

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The graphical representation is the point(s) where the lines of the equations intersect.

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What is the first step to solve the system: 3x - 4y = 12 and x = 2y - 8?

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Replace x with (−2y - 8) in the first equation.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution.

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What does it mean for two equations to be independent?

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Two equations are independent if they have exactly one solution.