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 no solutions?

Back

The lines representing the equations are parallel and never intersect.

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 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 using 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 both equations are satisfied.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

What does it indicate if two lines intersect at a point?

Back

The system has one unique solution.

Front

What is the result of solving the equation 4 = 7?

Back

It indicates no solution, as this statement is false.