Solving Systems of Equations Review

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What is a system of equations?

Back

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?

Back

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

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What is the graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations represent the solutions.

Front

What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a 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 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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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and intercepts of the lines represented by the equations.