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 if two lines are parallel when graphing a system of equations?

Back

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

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 coincide when graphing a system of equations?

Back

It means there are infinitely many solutions because the lines are the same.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

If the slopes of two lines are equal but the y-intercepts are different, what can be concluded?

Back

The system has no solution.

Front

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

Back

Two lines that intersect at exactly one point.

Front

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

Back

The equations represent the same line.

Front

How do you solve a system of equations graphically?

Back

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