System 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 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 a solution to a system of equations?

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A set of values for the variables that makes all equations true.

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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 an independent system of equations?

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A system with exactly one solution, where the lines intersect at one point.

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What is a dependent system of equations?

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A system with infinitely many solutions, where the equations represent the same line.

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What is an inconsistent system of equations?

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A system with no solution, where the lines are parallel.

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How do you find the solution of a system of equations using substitution?

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Solve one equation for one variable and substitute that expression into the other equation.

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How do you find the solution of a system of equations using elimination?

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Add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the substitution method?

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A method for solving systems of equations by substituting one variable with an expression from another equation.