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

It means the lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

The lines of the equations plotted on a coordinate plane.

Front

How do you find the solution to a system of equations by graphing?

Back

By identifying the point where the lines intersect.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x).

Front

What does a negative slope indicate about a line?

Back

The line decreases as it moves from left to right.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

If the lines are parallel and never intersect.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

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

Back

The lines coincide, meaning they are the same line.