Systems of Equations

Front

What are systems of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

Two lines that are parallel and never intersect.

Front

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

Back

Two lines that lie on top of each other, representing the same line.

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 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

What does it mean if two equations are dependent?

Back

The equations represent the same line, leading to infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

The equations represent different lines, leading to exactly one solution.