solve systems by graphing

Front

What is a system of linear equations?

Back

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

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are identical, meaning they lie on top of each other.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression derived from another equation.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.