Maths一問 Linear Equations in Three Unknown

最方便的方法就是使用Gaussian Elimination


圖片參考：http://i187.photobucket.com/albums/x22/cshung/700803250346.jpg

1).6x + y +z = 32__(1)

｛3x – 4y + 2z = 4___(2)

-8x – 3y+ 4z = 15 ____(3)

FROM (1) 32-6x-y=z
sub it into(2)
3x-4y+2(32-6x-y)=4
3x -4y +64 -12 - 2y = 4
-9x - 6y = -60
3x + 2y = 20
y=(20-3x)/2 ____(4)

Sub (4) into(3)
-8x-3((20-3x)/2 )+4(32-6x-((20-3x)/2 ))
-16x-60+9x+256-48x-80+12x=30
x=2
sub x=2 into y=(20-3x)/2
y=7
sub x & y into(1)
z=13



2)5x + 3y +z = 63____(1)

｛-2x- 6y + 4z = 18_____(2)

-3x + 5y –2z = -41______(3)

(1)+(2)+(3)
2y+3z=40____(4)
form(1).. z=63-3y-5x___(5)
sub (5) into (2)
-2x-6y+4(63-3y-5x)=18
-22x-18y+252=18
x=(234-18y)/22

sub x=(234-18y)/22 and (5) into(4)
2y+3(63-3y-5x)=40
2y+3(63-3y-5((234-18y)/22))=40
-154y+270y-3510=-3278
y=2
sub y=2 into(4)
z=12
LAST x=9

做呢些數都係整到全部interms of 其中一個unknown
跟住sub番入去
要小心d正負號
加減完就得