Types of Solutions from Systems of Equations

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 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, overlapping completely.

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing the intersection points.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely Many Solutions

Front

If two equations are identical, what can be said about their solutions?

Back

They have infinitely many solutions.

Front

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

Back

Two parallel lines that never intersect.

Front

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

Back

Two lines that intersect at a single point.