Question

Solve the system of linear equations. Show your work.
I'm obviously doing this all wrong since I just went through 3 pieces of paper and didn't get the right answers. :/

Answer 1

I would learn to use eliminator for 3 or more variables. (Using substitution can often be confusing..)

Here is an example
http://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices--reduced-row-echelon-form-1

Answer 2

in this problem, the first step could be: multiply the top row by -1 and add the result to the 2nd row to get a new 2nd row

Answer 3

okay, i did that.

Answer 4

what did you get ?

Answer 5

i got
x+y+z=5
8y+2z=12
-6y+z= -24

Answer 6

ok, looks good.

people often leave out the variables (but make sure we keep the same order x y z)
so (short hand) we have
1 1 1 5
0 8 2 12
0 -6 1 -24

Notice the first column has all zeros below the 1.
the next step is to zero out all the entries below the 8 in the 2nd column

if you have a calculator that does fractions, it is easier...
but the idea is multiply the 2nd row by 6/8 (this makes 6/8 * 8 = 6) and add the result to the third row. This will make the -6 in the 3rd row 0

can you do that ?

Answer 7

the 6/8 (or 3/4 or 0.75) times the 2nd row gives 0 6 1.5 9
we add that to the 3rd row to get a new 3rd row

Answer 8

i f you do the arithmetic correctly the new 3rd row is
0 -6 1 -24
+ 0 6 1.5 9
-------------
0 0 2.5 -15

and the problem is now
1 1 1 5
0 8 2 12
0 0 2.5 -15

Answer 9

if we put the variables back in you will notice that the last line is short for

2.5z = -15

you can solve for z

Answer 10

sorry i just dont understand that way.

Answer 11

There are 2 parts to understanding... one is learning the method without knowing why it works... if you can do that, you can at least solve these type problems.

Learning why it works is not hard, but I would make that a 2nd goal. The video helps fill in the details.

Answer 12

But if you are able to get to this
1 1 1 5
0 8 2 12
0 0 2.5 -15

you are almost done.
the last line says 2.5z= -15
divide both sides by 2.5 and you get z= -15/2.5= -6

the 2nd line says
8 y + 2z =12
but you know z is -6 so you have

8y +2(-6) = 12
8y -12 = 12
8y= 24
y=3

can you finish using the first row ?

Answer 13

you can always leave in the letters if that confuses you...