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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, overlapping completely.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the lines intersect on a graph.

Front

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

Back

Two lines that cross at a single point.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that never meet.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

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Two identical lines that lie on top of each other.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.