Systems of Equations 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 intersect at exactly one point.

Front

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

Back

The lines are parallel and never intersect.

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.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect on a graph.

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 is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

If two lines have the same slope but different y-intercepts, what can be said about their relationship?

Back

They are parallel lines and will never intersect.

Front

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

Back

No solution, as the lines are parallel.

Front

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

Back

(1, 3), as the lines intersect at this point.