Systems of Linear Equations

A system of linear equations is just a set of two or more linear equations.

There are three possibilities:

The lines intersect at zero points. (The lines are parallel.)

The lines intersect at exactly one point. (Most cases.)

The lines intersect at infinitely many points. (The two equations represent the same line.)

They may be solved Graphically as well as Algebraically, we will start Graphically...

There are four quadrants on in the cartesian plane (x and y-axis).

The first quadrant is the top right corner in the cartesian plane.

The second quadrant is the top left, the third is the lower left, and the fourth is the lower right side.

(They run counterclockwise)

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

Slope is written in y/x form (or rise/run)

This should seem like review for you at this point.

Note that the slope is the C.R.O.C., the Unit Rate, delta y over delta x...

Parallel lines never intersect and have the exact same slope.

Perpendicular lines intersect and their slopes have a special relationship in that they are negative reciprocals of each other

For example, 1/2 has a negative reciprocal of -2/1