Solving Systems

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 equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The equations represent lines that intersect at exactly one point.

Front

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

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

What does it mean for two lines to be skew?

Back

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

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The graph shows two overlapping lines.

Front

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

Back

The graph shows two intersecting lines at a single point.