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 to solve a system of equations?

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

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What is the elimination method?

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A technique for solving systems of equations by removing one variable, allowing for easier solving of the remaining equation.

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How do you determine which variable to eliminate in the elimination method?

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Choose the variable that has coefficients that can easily be made equal and opposite.

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What is the substitution method?

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A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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

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What does it mean for two lines to be parallel in the context of systems of equations?

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Parallel lines have the same slope but different y-intercepts, indicating that the system is inconsistent.

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What is the graphical method for solving systems of equations?

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Plotting the equations on a graph and identifying the point(s) where they intersect.