System 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 to graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you determine the solution from a graph?

Back

By identifying the coordinates of the point where the lines intersect.

Front

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

Back

A straight line where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The rate of change of y with respect to x; it indicates the steepness and direction of the line.

Front

What is the y-intercept of a line?

Back

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 are parallel?

Back

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

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, meaning there are infinitely many solutions to the system.

Front

How can you solve a system of equations by graphing?

Back

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