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 in a system of equations?

Back

They have no solutions because they never intersect.

Front

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

Back

They have infinitely many solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

They have one solution, which is the point of intersection.

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 of a line?

Back

The steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

If the slopes of two lines are equal and the y-intercepts are different, what can you conclude?

Back

The lines are parallel and have no solutions.

Front

If the slopes of two lines are different, what can you conclude?

Back

The lines intersect at one point and have one 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.