Solving 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 that are solved together.

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What does it mean for two equations to intersect on a graph?

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It means that the equations have a common solution, represented by the point where their graphs meet.

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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.

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What is a matrix in the context of systems of equations?

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A rectangular array of numbers used to represent a system of equations, allowing for efficient calculations.

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How do you represent a system of equations using matrices?

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By creating a coefficient matrix, a variable matrix, and a constant matrix.

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

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It means that the equations represent parallel lines that never intersect.

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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, so every point on the line is a solution.

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How can you check if your solution to a system of equations is correct?

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By substituting the solution back into the original equations to see if both equations are satisfied.

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What is the graphical method of solving systems of equations?

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A method where the equations are graphed, and the solution is the point of intersection.