Algebra Problem/Assignment

[orick]

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pwde pd na siya gamitan ug paagi using determinants.

[tahbiapo]

i'm on a roll kay gimingaw na ko'g math... hehe. below is a possible solution to the first problem. di raba whole numbers ang answers below, kundi approximations lang. nya, ang second equation 4x + y = 7, pag e-substitute na ang numbers, ang outcome kay 21 lagi. not even close to 7. so i guess this problem has no solution. () calculator ra sa cellphone ako gamit so please doublecheck.

x - 3y + 7z = 6
4x + y = 7
2x + 3y + z = 9

1 -3 7 6
4 1 0 7
2 3 1 9

1 -3 7 6
0 13 28 -17
0 9 -13 -3

1 0 8/3 5
0 13 28 -17
0 9 -13 -3

1 0 8/3 5
0 1 28/13 -17/13
0 9 -13 -3

1 0 8/3 5
0 1 28/13 -17/13
0 0 -421/13 114/13

1 0 8/3 5
0 1 0 -64545/71149
0 0 -421/13 114/13

1 0 8/3 5
0 1 0 -64545/71149
0 0 1 -114/421

therefore, x = 5 - (8/3)z
y = -64545/71149
z = -114/421
but, since 21 is not equal to 7, this problem has no solution. (??)

[juNexbOyz]

calculator....

[mikogerald]

Ah libog au kong e mata2x nato.hehe pro dili cya lisud.

[prakx]

hihi.. ahaka naa lagi in ani dre..

[akosabni]

^ bitaw? ... pero kong naka post pa ko ad2ng 2006 ... mo-apil ko ug post ...

tabangi ko ani beh.. lisud jud kaayo. Waaaa kinsay maka solve ani using matrices?

do your homework, man

[rambutan]

http://www.algebrahelp.com/

link ai.. mkatabang ni..

[123456]

yeah.. libog xa mata matahon..

[tackielarla]

Sorry. MAtrices man diay kinahanglan. Diko kibaw.

[cebu.opportunities]

Hello,

tabangi ko ani beh.. lisud jud kaayo. Waaaa kinsay maka solve ani using matrices?


(a) x - 3y + 7z = 6
4x + y = 7
2x + 3y + z = 9

(b) 3x - 5z = 1
2x + 3y = 6
x +y +z = 5

Thanks!

ang letter a nga problem, nakoy problem with the first equation pero ma sakto ang second and third equation. if ny sayop isa, sayop mn tanan. hmmm.

I'm using SGPMDAS principle lang. unsaon diay nang matrix/ces?

letter b problem:
(b) 3x - 5z = 1
2x + 3y = 6
x +y +z = 5

2x + 3y = 6
3y = 6 - 2x
y = 6/3 - 2/3 x
y = 3 - (2/3 x)
the same with ~~ y = 3 - (2x/3)

x + y + z = 5
z = 5 - x - y
z = 5 - x - [2 - (2/3 x)]
z = 5 - x - 2 + 2/3 x
z= (5 -2) - [(3/3 x) + (2/3 x)]
z = 3 - (1/3 x)
note: butangan lang nako parenthesis and bracket pra di malipat

extracting "x" using first equation: (pwede rasad using 2nd equation)
3x - 5y = 1
3x - 5 [3 - (1/3 x)] = 1
3x - 15 + (5/3 x) = 1
(9x/3) + (5x/3) = 1 +15
14x/3 = 16 ; multiply both sides by 3/14
x = 16 (3/14) ; fraction from the left side cancelled
x = 8 (3/7) ; reduce by dividing 2 both from denominator and numerator a.k.a. law of cancellation or elimination
x = 24/7

extracting "z" using first equation
3x - 5z = 1
-5z = 1 - 3x ; multiply both sides by "-"
5z = 3x - 1
z = (3x -1) / 5
z = (3/5)(24/7) - (1/5) ; substitution of variable x
z = (72/35) - (7/35)
z = (72-7) / 35 ; sorry for this, same as above lang ni. pa long cut lang, haha)
z = 65/35 ; reduce by dividing 5 both on denominator and numberator
z = 13/7

extracting "y" using the third equation: (second equation may also be used in extracting y)
x + y + z = 5
y = 5 - x - z
y = 5 - (24/7) - (13/7) ; substitution of variable "x" and "z"
y= (35- 24 - 13) / 7
y = -2/7

Checking the first equation:
3x - 5z = 1
3 (24/7) - 5 [3 - (1x/3)] = 1 ; substitution
72/7 - 15 + (5/3) (24/7) = 1 ; distribution
(72 - 105 + 40) / 7 = 1 ; principle in addition and subtraction in fractions
7/7 = 1
1= 1 Therefore, equation 1 is correct.

Checking second equation:
2x + 3y = 6
2 (24/7) + 3 (-2/7) = 6
(48-6) /7 = 6
42/7 = 6
6 = 6 Therefore, second equation is correct.

Checking third equation:
x + y + z = 5
24/7 + (-2/7) + 13/7 = 5
(24 - 2 + 13) / 7 = 5
35/7 = 5
5 = 5 Therefore, third equation is correct.

Three equations are correct so,
therefore

x = 24/7
y = -2/7
z = 13/7

weee, Love it!

PS: nindot ning ing.ani dah. di mn lang siya ky tungod assignment sa uban, it's wrong to help solve the problem. This thread was created many years ago so di na magamit sa TS but the steps used in solving ky makatabang jud. After all, lain2 mana equations manggawas during quizzes and exams. Hope others may also share other ways on solving this pra ma refresh atong huna2.