Essentials Graphing Systems of Equations

Front

What is the solution to a system of equations?

Back

The solution (x, y) is the point where the equations intersect.

Front

How is a coordinate pair ordered?

Back

A coordinate pair is ordered as (x, y).

Front

What does it mean if two lines intersect in a graph of a system of equations?

Back

It means the system has one unique solution.

Front

What is the graphical representation of a system of equations with no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same line, overlapping each other.

Front

If a system of linear equations has one solution, what does this mean about the two lines?

Back

The lines are intersecting lines.

Front

What is the y-intercept of a line in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of b, where the line crosses the y-axis.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x.

Front

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

Back

Substitute the point into both equations; if both are true, it is a solution.

Front

What is the purpose of graphing a system of equations?

Back

To visually find the point of intersection, which represents the solution.