中二數學功課問題(方程)(急)

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您好，我是 lop，高興能解答您的問題。

(1)

(3x+1)(Ax-3) ≡ 6x²+Bx+C
3x(Ax-3) + 1(Ax-3) ≡ 6x²+ Bx + C
3Ax^2 - 9x + Ax - 3 ≡ 6x²+ Bx + C
(3A)x^2 + (A-9)x - 3 ≡ 6x²+ Bx + C

3A = 6
(A-9) = B
-3 = C

Get A = 2 , B = -7 , C = -3 .

(2)

3x-1=4(y+1) --- (1)
7(2x+3)=6y --- (2)

From (1) :

3x - 1 = 4y + 4
3x - 5 = 4y
y = (3x-5)÷4 --- (3)

Sub (3) into (2) ,

7(2x+3) = 6(3x-5)÷4
4(7)(2x+3) = 6(3x-5)
56x + 84 = 18x - 30
56x - 18x = - 30 - 84
38x = -114
x = -3 --- (4)

Sub (4) into (3) ,

y = [3(-3)-5]÷4
y = (-9-5)÷4
y = -14÷4
y = -3.5

Answer : x = -3 , y = -3.5 .

(3)

5x-8=6(y+2) --- (1)
9(y-5)=-6x-21 --- (2)

From (1) :

5x - 8 = 6y + 12
5x = 6y + 20
x = (y+20)÷5 --- (3)

Sub (3) into (2) ,

9(y-5) = - 6(y+20)/5 - 21
5(9)(y-5) = -6(y+20) - 21(5)
45y - 225 = -6y - 120 - 105
45y + 6y = -225 + 225
51y = 0
y = 0 --- (4)

Sub (4) into (3) ,

x = (y+20)÷5
x = (0+20)÷5
x = 20÷5
x = 4

Answer : x = 4 , y = 0 .

(4)


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(5)

Let the original number is ( 100a + 10b + 4 ) .

a + b = 13 --- (1)
100b + 10a + 4 = 100a + 10b + 4 - 90 --- (2)

From (2) :

90b = 90a - 90
b = a - 1 --- (3)

Sub (3) into (1) ,

a + ( a - 1 ) = 13
2a = 14
a = 7 --- (4)

Sub (4) into (3) ,

b = a - 1
b = 7 - 1
b = 6

Answer : The original number is 764 .

2011-10-11 18:29:56 補充：
corrections (4) ,

x = -6

Answer : x = -6 , y = 4