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.

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

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The lines representing the equations are parallel and never 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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What does it mean if a system of equations has infinitely many solutions?

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

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How do you determine the best method to solve a system of equations?

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Consider the form of the equations; use substitution if a variable is isolated, and elimination if both are in standard form.

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What is the graphical interpretation of a system of equations?

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The solutions are the points where the graphs of the equations intersect.

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

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Substitute the solution back into the original equations to see if they hold true.

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

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A rectangular array of numbers that can represent the coefficients of a system of equations.

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What is the role of the determinant in solving systems of equations using matrices?

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The determinant helps determine if a unique solution exists; if it's zero, the system may have no or infinitely many solutions.