Intro to Systems

When you graph two or more equations on the same coordinate plane, you create a
SYSTEM of EQUATIONS,
also called SIMULTANEOUS EQUATIONS.

Notice the point where the lines are coming together?

This is a point all of the lines share in common; a point where all the lines are in the same place at the same time.

The ordered pair for this particular point is (8,-1).

The (x, y) ordered pair for this point is (8,-1).

If you plug in 8 for x and -1 for y in all of the equations, it will solve all of the equations simultaneously (at the same time).

Look at equation 1: y = 1/2x - 5

Replace x with 8 and y with -1: -1 = 1/2(8) - 5
*1/2 of 8 is 4 !
Simplify each side: -1 = 4 - 5
-1 = -1

To summarize, the Point of Intersection is the SOLUTION to the System of Equations.

There are 3 possible outcomes in a System of Equations:
1 Solution means there is one (x, y) ordered pair that will solve all equations. Graphically, there is ONE point of intersection.
NO Solution happens when the graphs are parallel lines. Since there is no point of intersection, you know there is NO solution.
INFINITE Solutions mean the lines for the equations are actually the same line (land on top of each other). Since they share every point, they have INFINITE Solutions.

Altogether now!
2 or more equations on the same plane create a SYSTEM.
The Point of Intersection is the ONE SOLUTION to the System of Equations.

No Intersection?
NO SOLUTION

Lines that share every point?
INFINITE SOLUTIONS