Basic 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 has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you determine if a point is a solution to a system of equations?

Back

The (x,y) coordinates must satisfy both equations.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines representing the equations.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

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

Front

What is an independent system of equations?

Back

A system where the equations represent different lines, resulting in exactly one solution.

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.