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 lines representing the equations intersect at exactly one point.

Front

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 coincide, meaning they are the same line.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

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 other.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where all equations are satisfied.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.