Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the lines represented by the equations intersect at exactly one point.

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, so every point on the line is a solution.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the graphical representation of the solution to a system of equations?

Back

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

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

Front

How can you determine if a system of equations has no solution by graphing?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

How can you determine if a system of equations has infinitely many solutions by graphing?

Back

If the lines overlap completely, they represent the same line, indicating infinitely many solutions.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

Back

No solution (the lines are parallel).