3.4 Solving equationsSimultaneous equations

Snakes on planesor

How to describe the geometric relationship between planes

Once upon a time there was a plane called snakes….

Let’s call it 2x + 4y + 3z = 10

A point that would sit on this plane is(x, y, z) = (2, 0, 2)

x

y

z

The plane then cloned himself…

2x + 4y + 3z = 102x + 4y + 3z = 102x + 4y + 3z = 10

And tried to hide the fact that he wasn’t as different as he

thought….

2x + 4y + 3z = 104x + 8y + 6z = 2010x + 20y + 15z = 50

But then decided on being inconsistent instead……

2x + 4y + 3z = 10

4x + 8y + 6z = 3010x + 20y + 15z = 70

And being inconsistent changed his mind again……

2x + 4y + 3z = 10

4x + 8y + 6z = 30x + 2y + 3z = 15

Story recapWrite a system of three linear equations with three variables to represent the following geometric situations:

Three planes parallelThree planes become one!Two planes parallel with the third plane intersecting both planes

Snakesy wanted to prove how unique he was so found two other planes with nothing in common

with him……

2x + 4y + 3z = 10x – 2y + 5z = 84x - 3y - 2z = -10

But then decided it would be nice to be dependent on some

friends…..

2x + 4y + 3z = 10

3x - 2y + 3z = 205x + 2y + 6z = 30

But also didn’t want anyone to know that he needed a little help

from his friends……

4x + 8y + 6z = 20

3x - 2y + 3z = 205x + 2y + 6z = 30

So decided to elevate himself above his friends and be once

again inconsistent!

2x + 4y + 3z = 10

3x - 2y + 3z = 205x + 2y + 6z = 30

2x + 4y + 3z = 40

Story recapWrite a system of three linear equations with three variables to represent the following geometric situations:

Three planes that meet in a lineThree planes that intersect at one point onlyTwo planes meet in a line that is parallel to the third plane