Systems of Linear Equations

Systems of Linear Equations

SWS Algebra

Vocabulary

• Systems of Linear Equations

• Quadrants, x and y axis

• y = mx + b

• Slope and Y-intercept

• Parallel and Perpendicular Lines

Multiple Select

Which terms do you remember already learning about?

• Systems of Linear Equations

• Quadrants

• Slope-Intercept Form

• Parallel versus Perpendicular Slopes

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...

Open Ended

Considering two lines were not the same line, could they ever intersect more than one time and less than infinitely many times? Explain why or why not...

Quadrants

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)

Multiple Choice

If I had a point that had a positive x_value and a negative y-value which quadrant would that be in?

• I

• II

• III

• IV

Slope-Intercept Form

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...

Open Ended

How do I know if something is linear or not? Make sure you use complete sentences.

Parallel versus Perpendicular slopes

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

Open Ended

Using complete sentences, give two real life examples of parallel lines and perpendicular lines in everyday life (one of each).