Systems of Equations Flashcard: Graphing and Substitution

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on the same coordinate plane.

Front

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

Back

It represents the solution to the system, where all equations are satisfied.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

Front

What does it mean for two equations to be dependent?

Back

They represent the same line and have an infinite number of solutions.

Front

What does it mean for two equations to be independent?

Back

They represent different lines and have either one solution or no solutions.