Systems of Equations - Special Solutions

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 lines representing the equations are parallel and never intersect.

Front

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

Back

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

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 is the graphical representation of parallel lines?

Back

Lines that run in the same direction and never meet.

Front

What is the graphical representation of intersecting lines?

Back

Lines that cross each other at one point.

Front

What is the graphical representation of the same lines?

Back

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

Front

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

Back

If the equations are in the form of parallel lines.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations are identical, resulting in the same line.

Front

What is the solution to the system of equations: y = 2x + 3 and y = 2x - 1?

Back

No Solution (the lines are parallel).