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 that are solved together.

Front

What does it mean for two lines to be parallel in a graph?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

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

Back

Two lines that intersect at exactly one point.

Front

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

Back

The lines are parallel and do not intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

Two lines that lie on top of each other (are coincident).

Front

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

Back

By identifying the point(s) where the lines intersect on the graph.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean if two lines have different slopes?

Back

They will intersect at exactly one point, indicating a unique solution to the system.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where the values of the variables satisfy all equations.