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 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 substitution method?

Back

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

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What is the elimination method?

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A method of solving a system of equations by adding or subtracting equations to eliminate one variable.

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When is substitution the best method to use?

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When one equation is already solved for one variable.

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What does it mean if two equations represent the same line?

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They have infinite solutions.

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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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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.