Systems by Graphing

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 two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

The system has no solution.

Front

What does it mean if two lines coincide?

Back

The system has infinitely many solutions.

Front

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

Back

By analyzing the graphs of the equations.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines representing the equations.

Front

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

Back

(1, 3)

Front

If a system of equations has no solution, what can be said about the lines?

Back

The lines are parallel and will never intersect.

Front

If a system of equations has infinitely many solutions, what can be said about the lines?

Back

The lines are the same line, coinciding with each other.

Front

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

Back

No solution.