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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

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.

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

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

Back

If the lines are parallel, the system has no solution.

Front

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

Back

If the lines overlap completely, the system has infinitely many solutions.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.