Systems Of Equations Elimination and Substitution

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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 to solve a system of equations?

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

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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.

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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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How do you check if a solution is correct for a system of equations?

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

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What is the graphical interpretation of a system of equations?

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The solution is the point where the graphs of the equations intersect.

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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 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 can you identify a system of equations that is dependent?

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If the equations are multiples of each other, they are dependent and have infinitely many solutions.

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How can you identify a system of equations that is independent?

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If the equations represent different lines that intersect at one point, they are independent and have a unique solution.