Systems of Equations: 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 are parallel?

Back

They have the same slopes and different y-intercepts.

Front

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

Back

The system has one unique solution.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the lines intersect on a graph.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, overlapping each other.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x).

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.