System of Equations Graphs

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

It means that the lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the lines representing the equations coincide, or are the same line.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By analyzing the intersection points of the lines on a graph.

Front

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

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never intersect.

Front

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

Back

Two 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 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, making it easier to solve for the other.