Solving Systems with Three Variables

Front

What is a system of linear equations?

Back

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

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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 there are countless points of intersection.

Front

How do you determine if a system of equations has a unique solution?

Back

If the equations represent lines that intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where intersections represent solutions.

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?

Back

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

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What is a consistent system of equations?

Back

A system that has at least one solution.

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What is an inconsistent system of equations?

Back

A system that has no solutions.

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What is a dependent system of equations?

Back

A system where the equations represent the same line, resulting in infinitely many solutions.