Solving Systems by Graphing

Front

What is the solution to a system of equations when graphed?

Back

The point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

How many solutions can a system of equations have?

Back

A system can have one solution, no solution, or infinitely many solutions.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, meaning there is no solution to the system.

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

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.

Front

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

Back

The lines coincide, meaning they are the same line and intersect at every point along that line.

Front

How can you find the solution to a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the point of intersection.

Front

What is the significance of the point (1, 3) in a system of equations?

Back

It is a solution to the system, meaning it satisfies both equations.