聯立二元一次方程

1.
設該數為(10a + b) [a是十位數字,b是個位數字]

十位數字是個位數字的2倍
∴a = 2b--------------(1)

十位數字與個位數字對調後,所得的數字比原數小9
∴10a + b = 10b + a + 9
∴9a - 9b = 9
a - b = 1----------------(2)

將(2)代入(1): 2b - b = 1
b = 1

將b=1代入(1): a = 2

∴原數為21

2.
設健雄和啟智各有a和b張地契

健雄說:[如果你給我一張地契,那麼我和你有的地契數目便會一樣。]
∴a + 1 = b - 1
a - b = -2-------------------(1)

啓智說:[還是你給我一張地契吧!那麼有的地契便是你的2倍了。]
∴b + 1 = 2(a - 1)
b + 1 = 2a - 2
2a - b = 3-------------------(2)

(2)-(1): a = 5
將a=5代入(2): 2×5 - b = 3
b = 7
∴健雄和啟智各有5和7張地契

3.
設a和b分別為父、子現時的年齡

父親年齡的一半比兒子年齡還要多9歲
∴a÷2 - b = 9
a - 2b = 18--------------------------(1)

3年後,父親年齡的三分一正是那時兒子的年齡
a+3 = 3(b+3)
a + 3 = 3b + 9
a - 3b = 6---------------------------(2)

(1)-(2): b = 12

將b=12代入(2):
a - 3(12) = 6
a = 42

∴父、子現時分別為42和12歲

2008-02-10 17:45:31 補充：
4. x/2-y=1/6------------(1)x/3+2y=1------------(2)由(1),y = x/2 - 1/6------------(3)將(3)代入(2):x/3+2(x/2 - 1/6)=1x/3 + x - 1/3 = 1x + 3x - 1 = 34x = 4x = 1將x=1代入(3):y = 1/2 - 1/6y = 1/3

2008-02-10 17:46:11 補充：
5. x=3/2y--------------(1)4x-5y=4------------(2)將(1)代入(2):4(3/2y) - 5y = 46y - 5y = 4y = 4將y=4代入(1):x = 3/2(4)x = 6

2008-02-10 17:46:47 補充：
6. 2x-3y=0------------(1)x+5y-13=4--------(2)由(2),x = 17 - 5y------------(3)將(3)代入(2):2(17 - 5y) - 3y = 034 -10y - 3y = 013y = 34y = 17/7將y=17/7代入(3):x = 17 - 5(17/7)x = 34/7

2008-02-10 17:47:03 補充：
7. X Y=35---------(1)3x 5y=120----(2)由(1),x = 35 - y------------(3)將(3)代入(2):3(35 - y) 5y=120105 - 3y 5y = 1202y = 15y = 7.5將y=7.5代入(3):x = 35 - 7.5x = 27.5

(1)
設個位數為x, 十位數為y
y = 2x ------(1)
10y+x - 9 = 10x +y
=> y = x+1 -------(2)
Sub (1) into (2):
2x = x+1
x = 1, y = 2
原數=12
(2)
設健雄的地契數目為x,啟智的地契數目為y
x+1 = y ----(1)
2(x-1) = y -----(2)
sub(1) into (2):
x+1 = 2(x-1)
x = 3, y = 4
健雄有3張地契
啟智有4張地契
(3)
設兒子現時年齡為x, 父親現時年齡為y
y/2 = x +9 -----(1)
(y+3)/3 = x+3 -------(2)
Sub (1) into (2):
[2(x+9) +3]/3 = x+3
2x + 18 + 3 = 3x + 9
x = 12
y = 42
父親現年=42歲、兒子現年=12歲

1.設十位數=x，個位數=y
x=2y，10x+y=10y+x+9
解方程式:x=2，y=1

2.設健雄有地契x張，啟智有地契y張
x+1=y-1 ，2(x-1)=y+1
解方程式:x=5，y=7

3.設父為x歲，子為y歲
x/2 =y+9，x+3/3 = y+3
解方程式:x=42，y=12