graphing systems

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.

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 the solution to the system y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system y = 1/2x + 2 and y = -3x + 9?

Back

(2, 3)

Front

If two lines are graphed and they intersect at the point (-3, -8), what does this indicate?

Back

This point is the solution to the system of equations represented by the lines.

Front

What happens when you graph the same equation twice?

Back

You will have infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection of the graphs of the equations.