F.2 Maths(二元一次方程),(15分)

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

(1)
3x - 1 = 4y + 4
4y = 3x - 5
y = (3x - 5)/4 ...... (3)

Put (3) into (2):
7(2x + 3) = 6(3x - 5)/4
28(2x + 3) = 6(3x - 5)
14(2x + 3) = 3(3x - 5)
28x + 42 = 9x - 15
19x = -57
x = -3

Put x = -3 into (3):
y = [3(-3) - 5]/4
y = -7/2

Ans: x = -3, y = -7/2


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

(1):
5x - 8 = 6y + 12
5x - 6y = 20 ...... (3)

(2):
9y - 45 = -6x - 21
6x + 9y = 24
4x + 6y = 16 ...... (4)


(3) + (4):
9x = 36
x = 4

Put x = 4 into (3):
5(4) - 6y = 20
y = 0

Ans: x = 4, y = 0


3.
(x + 9)/3 - (y - 10)/2 = 4 ...... (1)
x + 5y/2 = 4 ...... (2)

(1):
2(x + 9) - 3(y - 10) = 24
2x + 18 - 3y + 30 = 24
2x - 3y = -24 ...... (3)

(2):
2x + 5y = 8 ...... (4)

(4) - (3):
8y = 32
y = 4

Put y = 4 into (4):
2x + 5(4) = 8
x = -6

Ans: x = -6, y = 4


4.
x/3 + y/4 - 3/2 = 0 ...... (1)
7x/12 - (y + 12)/8 = 0 ...... (2)

(1) x 12:
4x + 3y - 18 = 0 ...... (3)

(2) x 24:
14x - (y + 12)3 = 0
14x - 3y - 36 = 0 ...... (4)

(3) + (4):
18x - 54 = 0
x = 3

Put x = 3 into (3):
4(3) + 3y - 18 = 0
3y = 6
y = 2

Ans: x = 3, y = 2


5.
Let the price of a black ball-pen be $x, and that of a blue ball pen be $y.

5x + 7y = 48 + 2 ...... (1)
7x + 5y = 48 - 2 ...... (2)

(1) x 7:
35x + 49 = 350 ...... (3)

(2) x 5:
35x + 25y = 230 ...... (4)

(3) - (4):
24y = 120
y = 5

Put y = 1 into (1):
5x + 7(5) = 48 + 2
5x + 35 = 50
x = 3

Ans: The price of a black ball-pen is $3, and that of a blue ball pen is $5.


6.
Let the numbers of questions Sections A and B be a and b respectively.

a + b = 40 ...... (1)
2a + 3b = 92 ...... (2)

(1):
b = 40 - a ...... (3)

Put (3) into (2):
2a + 3(40 - a) = 92
120 - a = 92
a = 28

Put b = 28 into (1):
(28) + b = 40
b = 12

Ans: There are 28 questions in Section A, and 12 questions in Section B.
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