Solving Systems Algebraically

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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 simultaneously.

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What does it mean to solve a system of equations algebraically?

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It means to find the values of the variables that satisfy all equations in the system using algebraic methods.

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What is the Elimination Method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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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 does it mean when 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 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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How do you determine if a system of equations has no solution?

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If you arrive at a false statement, such as 4 = 7, when trying to solve the system.

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The system has infinitely many solutions (dependent system).