Mathematics

[WiseKran]

Hello.

Ive had a Math assignemente that I don\'t Understand.

I was hoping someone could explain these few problems to me, how to do them.

Solve the Following System of Equations.
3x + 4y + z = 17
2x + 3y + 2z = 15
x + y =4

How Would I find the axis of symmetry on:
y = 2x^2 - 4x + 11


And lastly, How do I factor
x^2 + 10x - 24 = 0





These are the 3 That I could not understand from review, Most likely I knew how to do them at one time. But I have since forgotten

[steuben]

last one is the quadratic formula (b+/-sqrt(b^2-4ac))/2a

first one is solve the matix of
|3 4 1 17|
|2 3 2 15|
|1 1 0 4  |
such that you get
|1 0 0 _|
|0 1 0 _|
|0 0 1 _| with somthing the fourth column
or you could do simple symbol juggling and subsitution

not sure about the second one.

[Drey]

steuben seems to have given overly complicated answers...

with the first just jiggle them about and put them into each other so use  x + y =4 and change it to x=4-y put that into the top one get another equation put that into the middle one get a value use that to work out the others

stuffs... (one of the equations was writen wrong but i fixed it later on)

z=2
y=3
x=1

with the second symetry is at -b/2a

in this case -(-4)/4 so 4/4 which is one. (x=1)

to factorise that... you need numbers that add to ten and times to -24

so that would be 12 and minus 2 or something
(x-2)(x+12) the roots being... 2 or -12

or

(x+2)(x-12) meaning x= -2 or 12

sketch it to work which is which?

[Daelor]

1. There are a number of ways to solve this, i\'ll use Cramer\'s Rule

A) Find the determinant of the coefficient matrix we\'ll name it Matrix A
 |3  4  1|
 |2  3  2|
 |1  1  0|
This equals: 1

Because this is one, we dont have to worry about the division of the substitution matrix, we can just find the determinants of those, so: for x:
 |17  4  1|
 |15  3  2|
 |1   1   0|
This equals one as well, so x=1
for y:

 |3  17  1|
 |2  15  2|
 |1   4   0|
This equals 3, so y=3
and z:
 |3  4  17|
 |2  3  15|
 |1   1   4|
This equals 2, so z=2

Solved!

Notation usage: the \"|\" symbol is used to denote the determinant of the matrix of numbers enclosed.

Edit...i was going to include the other solutions, but I was beaten to it

I agree with the other answers already posted as well...
#2 is the line at x=1
#3 is (x-2)(x+12)

[Drey]

if hes not understanding simple quardratics i dont think theres much point throwing matrixes at him :P

[Daelor]

Originally posted by Drey
if hes not understanding simple quardratics i dont think theres much point throwing matrixes at him

Yeah, I think your proably right, I just used what popped into my head first

The great things with problems like that though is that there are many ways to solve them: Cramer\'s rule, inverse matricies, algebraic substitution, graphically, etc.  You can go about solving the equation completly differently and still arrive at the same answer, thats one of the great features of algebra.  Very fun

edit: Included the quote of whom I am referring to for clarification.

[steuben]

Originally posted by Drey
(x-2)(x+12) the roots being... 2 or -12

is the answer because the 10 is positive. no need to sketch.

and they are not complex. just awkwardly written becuase there is no easy way to write the quad formula in plain text. and simple to use.

but a=1,b=10, c=-24. plug in the numbers to the formula and crunch away.

[Drey]

Originally posted by Daelor
The great things with problems like that though is that there are many ways to solve them Cramer\'s rule, inverse matricies, algebraic substitution, graphically, etc.  You can go about solving the equation completly differently and still arrive at the same answer, thats one of the great features of algebra.  Very fun

yep yep \\o/

[WiseKran]

Originally posted by Drey
steuben seems to have given overly complicated answers...

with the first just jiggle them about and put them into each other so use  x + y =4 and change it to x=4-y put that into the top one get another equation put that into the middle one get a value use that to work out the others

stuffs... (one of the equations was writen wrong but i fixed it later on)

z=2
y=3
x=1

Thank you everyone.

I think I understand the first one best the Way it was explained above.

the second and third I caught onto fast, as soon as I saw what formulas you had used ( I forgot them ).


Thank you for the help

[Rolf Blacksmith]

A pity this forum doesn\'t support TeX.

Would give you wonderfully written formulas ...

[LigH]

How about MathML?