急! F5 About equations 1exq03

16.
(a)
2x+ y = 5 ...... [1]
x +y² = 10 ...... [2]

(b)
[2]*2 :
2x + 2y² = 20 ...... [3]

[3] - [1] :
2y² - y = 15
2y² - y - 15 = 0
(2x + 5)(y - 3) = 0
x = -5/2(rejected) or y = 3

Put y = 3 into [1] :
2x + 3 = 5
x = 1
Hence, x =1 and y =3


17.
Let d be the denominator of the original fraction.

(7 + 2)/(d + 2) = (7/d) + (1/20)
[9/(d + 2)] - (7/d) = 1/20
[9d - 7(d + 2)]/[d(d + 2)] = 1/20
20(2d - 14) = d(d + 2)
40d - 280 = d² + 2d
d² - 38d + 280 = 0
(d - 10)(d - 28) = 0
d = 10 or d = 28(rejected)

The original fraction = 7/10


18.
(a)
Width of the original rectangle = 224/x cm
Width of the new rectangle = (224/x) + 1 cm

(x - 1)[(224/x) + 1] - 224 = 1
(x - 1)(224 + x)/x = 225
x² + 223x - 224 = 225x
x² - 2x - 224 = 0
(x - 16)(x + 14) = 0
x = 16 or x = -14(rejected)

Hence, x = 16