Graphing 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 two lines are parallel when graphing a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

What does it mean if two lines are the same when graphing a system of equations?

Back

It means the system has infinitely many solutions because every point on the line is a solution.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the two lines intersect.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run.

Front

What does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

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

Back

The lines are parallel.

Front

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

Back

The lines are the same.

Front

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

Back

(1, 3) - The point where the two lines intersect.