Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to have one solution?

Back

It means that the graphs of the equations intersect at exactly one point, indicating a unique solution for the variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the graphs of the equations are parallel and never intersect, indicating that there are no values for the variables that satisfy both equations.

Front

How do you find the slope of a line from its graph?

Back

The slope is calculated as the rise over run, or the change in y divided by the change in x between two points on the line.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, y).

Front

How can you graph a system of equations?

Back

To graph a system of equations, plot each equation on the same coordinate plane and look for points of intersection.

Front

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

Back

Two lines that intersect at a single point.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two lines that lie on top of each other, representing the same line.

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.