Systems of Linear Equations (with special cases)

Front

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

Back

The system has no solution if the graphs of the equations are parallel lines, meaning they never intersect.

Front

What does the graph of a system with infinitely many solutions look like?

Back

The graph consists of the same line represented by different equations, meaning every point on the line is a solution.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables.

Front

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

Back

A system has one solution if the graphs of the equations intersect at exactly one point.

Front

What is the solution to the system of equations: -6x + y = 6 and -3x + y = 6?

Back

The solution is (0, 6).

Front

What does it mean if two lines are skew?

Back

Skew lines are lines that do not intersect and are not parallel, typically found in three-dimensional space.

Front

How many solutions does the system have if the equations represent the same line?

Back

The system has infinitely many solutions.

Front

What is the graphical representation of a system with no solutions?

Back

The graphical representation consists of parallel lines.

Front

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

Back

The point of intersection represents the solution to the system, where both equations are satisfied.

Front

What is a consistent system of equations?

Back

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