Solving Systems of Equations Review

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical representation of a system of equations?

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The point(s) where the graphs of the equations intersect.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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How do you determine if a system of equations has no solution?

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If the equations represent parallel lines, they will never intersect, indicating no solution.

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How do you determine if a system of equations has infinitely many solutions?

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If the equations represent the same line, every point on the line is a solution.

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What is the solution to the system: y = 2x + 3 and y = -x + 1?

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(2, 7) - The point where the two lines intersect.

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What is the solution to the system: 3x + 4y = 12 and 6x + 8y = 24?

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Infinitely many solutions - the second equation is a multiple of the first.

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What is the first step in solving the system: 2x + 3y = 6 and x - y = 2?

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Use the elimination or substitution method to express one variable in terms of the other.