Solutions to Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

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How many solutions can a system of equations have?

Back

A system of equations can have one solution, no solution, or infinitely many solutions.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the graphical representation of a system with one solution?

Back

The graphical representation is two lines that intersect at a single point.

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What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by eliminating one variable to solve for the other.

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What is the substitution method?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What are parallel lines?

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Parallel lines are lines in a plane that never meet; they have the same slope but different y-intercepts.

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What are intersecting lines?

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Intersecting lines are lines that cross each other at one point, indicating a unique solution to the system.

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What are skew lines?

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Skew lines are lines that do not intersect and are not parallel; they exist in different planes.