MATHS!!!!!!!!F.2,3

1)If A= x+xy/2 and B=x+2xy/3,express y in terms of A and B.

2)(a) If 5A=h+3AB and 2B=h-7AB,express B in terms of A ONLY.

Q1.
If A = x + xy / 2, then
2A = 2x + xy
2A = x (2 + y)
x = 2A / (2 + y)
If B=x+2xy/3, then
3B = 3x + 2xy
3B = x(3 + 2y)
x = 3B / (3 + 2y)
Therefore,
x = 2A / (2 + y) = 3B / (3 + 2y)
將兩邊分母乘返返去對面，變成了：
2A(3 + 2y) = 3B(2 + y)
6A + 4Ay = 6B + 3By
4Ay - 3By = 6B - 6A
y (4A - 3B) = 6B - 6A
所以
y = (6B - 6A) / (4A - 3B)
同你個答案一樣。
總之，做親呢類問題，看看有甚麼要消失，就嘗試將條式整返做要消失的那一樣東西去。
2)(a) If 5A=h+3AB and 2B=h-7AB,express B in terms of A ONLY.

其實都係做返類似嘅嘢，因為這一次唔要 h ，所以就把兩條式都砌返個 h 出來：
5A=h+3AB ==> h = 5A - 3AB
2B=h-7AB ==> h = 2B + 7AB
所以
5A - 3AB = 2B + 7AB
好啦，因為要 express B in terms of A only，即係唔要 B，所以就把有 B 的擺埋一邊：
2B + 7AB + 3AB = 5A
2B + 10 AB = 5A
B (2 + 10A) = 5A
所以：
B = 5A / (2 + 10A)
同你個答案一樣，加前加後無乜分別。

(b)Hence, find the value of B if A=1.

照 sub 返 A = 1，你自己都識得計啦。
When A = 1,
B = 5A / (10A + 2) = (5 x 1) / (10 x 1 + 2) = 5 / 12
計完。

1) A=x+xy/2 B=x+2xy/3
2A=2x+xy 3B=3x+2xy
2A=x(2+y) 3B=x(3+2y)
x =2A/(2+y) x=3B/(3+2y)
so, 2A/(2+y) = 3B/(3+2y)
6B+3By = 6A+4Ay
6B-6A = (4A-3B)y
y=(6B-6A)/(4A-3B)

2a) 5A=h+3AB 2B=h-7AB
h=3AB-5A h=7AB-2B
so, 3AB-5A=7AB-2B
5A=10AB+2B
5A=B(10A+2)
B=5A/(10A+2)
2b) if A=1.
B=5/(10+2)
B=5/12

hope it can help you~~