問2題數學題~

1.
3x+y=11..............(1)
-3x+2y=10............(2)

(1) + (2):
3x + y - 3x + 2y = 11 + 10
3y = 21
y = 7 //

Sub. y = 7 into (1)
3x + 7 = 11
3x = 4
x = 4/3 //

2.
5x-y=16 ...............(1)
5x-3y=8 ...............(2)

(1) - (2)
5x - y - 5x + 3y = 16 - 8
2y = 8
y = 4 //

Sub. y = 4 into (1)
5x - 4 = 16
5x = 20
x = 4 //

2007-02-11 11:35:45 補充：
除左可以 eliminate 個 x 之外, 你仲可以 eliminate 個 y ~1.3x+y=11..............(1)-3x+2y=10............(2)(1) x 2 : 6x + 2y = 22.......(3)(3) - (2): 6x + 2y + 3x - 2y = 22 -109x = 12x = 4/3 //Substitute x = 4/3 into (1)4 + y = 11y = 7 //

2007-02-11 11:36:10 補充：
2.5x-y=16 ...............(1)5x-3y=8 ...............(2)(1) x 3 : 15x - 3y = 48.............(3)(3) - (2): 15x - 3y - 5x + 3y = 48 - 810x = 40x = 4 //Substitute x = 4 into (1)20 - y = 16-y = -4y = 4 //

2007-02-11 11:44:31 補充：
雖然在這兩題中 eliminate 個 y會較花時間, 但係始終都係一個解法, 參考一下亦無妨~當然, 考試時應選擇一個較快的方法啦~除此之外, 計完一個unknown之後, 你應該選擇一條最易的equation去substitute, 解埋另一個unknown~sorry, 我漏左一樣野未寫的, 就係解出2個 unknowns 後, 需寫番: The solution is x = ???, y = ???

１） 3x+y=11----(i)
-3x+2y=10----(ii)

(i) + (ii), 3x+y+(-3x+2y)=21
3y = 21
y = 7
sub y=7 into (i), 3x + 7 = 11
3x = 4
x = 4/3

２） 5x-y=16 ---(i)
5x-3y=8 ---(ii)

(i) - (ii), 5x-y-(5x-3y) = 8
2y = 8
y = 4
sub y=4 into (i), 5x - 4 = 16
5x = 20
x = 4

(1)
3x+y=11---(1)
-3x+2y=10---(2)
(1)+(2):3y=21
y=7---(3)
Sub (3) into (1)
3x+7=11
3x=4
x=4/3
Therefore x=4/3,y=7
Verification:
For (1),
L.H.S.=3x+y=3(4/3)+7=11=R.H.S.
For (2),
L.H.S.=-3x+2y=-3(4/3)+2(7)=10=R.H.S.
Verification completed

(2)
5x-y=16---(1)
5x-3y=8---(2)
(1)-(2):2y=8
y=4---(3)
Sub (3) into (1)
5x-4=16
5x=20
x=4
Therefore x=y=4
Verification:
For (1),
L.H.S.=5x-y=5(4)-4=16=R.H.S.
For (2),
L.H.S.=5x-3y=5(4)-3(4)=8=R.H.S.
Verification completed.