Graphing Systems of Equations

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 the same coordinate plane to find their intersection points.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines are the same.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the ordered pair into both equations; if it satisfies both, it is a solution.

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 rate of change of y with respect to x, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

How do you find the intersection point of two lines graphically?

Back

Locate the point where the two lines cross on the graph.