Essentials 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 points in common, meaning there is no solution.

Front

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

Back

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

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables.

Front

How can you tell if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and will never intersect.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis.

Front

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

Back

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