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 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 equations represent the same line, so every point on the line is a solution.

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

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

Back

If the lines intersect at exactly one point, the system has one unique solution.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a coordinate plane.

Front

What does it mean if two lines are skew?

Back

Skew lines are lines that do not intersect and are not parallel, existing in different planes.

Front

How can you tell if a system of equations is consistent?

Back

A consistent system has at least one solution, either one solution or infinitely many solutions.

Front

What is the purpose of graphing a system of equations?

Back

To visually find the point(s) of intersection, which represent the solution(s) to the system.