System Of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean when a system of equations has one solution?

Back

It means the graphs of the equations intersect at exactly one point.

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What does it mean when a system of equations has no solution?

Back

It means the graphs of the equations are parallel and never intersect.

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What does it mean when a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so they intersect at every point on that line.

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How can you solve a system of equations?

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You can solve it by substitution, elimination, or graphing.

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What is the substitution method?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical method of solving a system of equations?

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Plotting the equations on a graph and identifying the point(s) of intersection.

Front

If two lines are parallel, what can be said about the system of equations they represent?

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The system has no solution.

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If two lines coincide, what can be said about the system of equations they represent?

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The system has infinitely many solutions.