Solving Systems of Equations 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 for a system of equations to have a unique solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means the lines are the same, overlapping each other.

Front

How do you determine the solution of a system of equations by graphing?

Back

By finding the point where the lines intersect on the graph.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line with slope m and y-intercept b.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

How can you identify if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into both equations and checking if they hold true.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

What is the x-intercept of a line?

Back

The point where the line crosses the x-axis (y=0).