Systems of Equations

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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.

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What does it mean for a point to be a solution to a system of equations?

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It means that the point satisfies all equations in the system.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines or curves that intersect at points.

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What does it indicate if two lines in a system of equations are parallel?

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It indicates that the system has no solution.

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

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By analyzing the graphs of the equations: one intersection point indicates one solution, no intersection indicates no solution, and infinite intersections indicate infinitely many solutions.

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What is an ordered pair in the context of systems of equations?

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An ordered pair is a pair of numbers (x, y) that represents a point on the coordinate plane.

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What is the solution of a system of equations?

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The solution is the ordered pair that satisfies all equations in the system.

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

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It means that the equations represent the same line, and every point on that line is a solution.

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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 that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.