Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line.

Front

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

Back

By finding the point(s) where the graphs of the equations intersect.

Front

What are intersecting lines in the context of systems of equations?

Back

Lines that cross each other, indicating one unique solution.

Front

What are parallel lines in the context of systems of equations?

Back

Lines that never meet, indicating no solution.

Front

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

Back

Two equations represented by the same line.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then 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.