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New Trend Mathematics (2nd Edition) S2A - Chapter Quiz - Chapter 4
6
© 2009 Chung Tai Educational Press. All rights reserved.
Solution 1. (a) 13 −= xy
x 1 3 4 y 2 8 11
92 =+ yx 3A x 2 3 4
y 5 3 1
(b)
O
9
5
10
11
y
1 2 3 4x
1
2
3
4
6
7
8
y = 3x − 1
2x + y = 9
(c) In the graph, two straight lines intersect at (2, 5). ∴ The solution of the simultaneous equations is 2=x , 5=y . 2A
2. ⎩⎨⎧
−=
=+
)2(..........632)1(..........432
yxyx
(1) − (2),
3113
634232)63(42)32(
−=
−=
+−=−+
−−=−+
y
yyxyxyxyx 2M
Substitute
31
−=y into (1),
2552
4)31(32
=
=
=−+
x
x
x 2M
∴ The solution of the simultaneous equations is
25
=x , 31
−=y . 2A
5A
2A
2A
New Trend Mathematics (2nd Edition) S2A - Chapter Quiz - Chapter 4
7
© 2009 Chung Tai Educational Press. All rights reserved.
3. ⎩⎨⎧
=+
=−
)2(...........................252)1(.............................53
yxyx
From (2), )3(............225 yx −= 2M
Substitute (3) into (1),
1070756755)225(3
=
=
=−−
=−−
yyyyyy 2M
Substitute 10=y into (3),
5
)10(225=
−=x 2M
∴ The solution of the simultaneous equations is 5=x , 10=y . 2A
4. Rewrite the simultaneous equations as follows:
⎩⎨⎧
−=−+
−=−
)2(.................71156)1(.........................723
yxyx
(1) × 2, )3(...........1446 −=− yx 2M
(2) − (3),
21897461156
)14(7)46()1156(
=
=
=+−−+
−−−=−−−+
yyyxyxyxyx 2M
Substitute 2=y into (1),
1337)2(23
−=
−=
−=−
xx
x 2M
∴ The solution of the simultaneous equations is 1−=x , 2=y . 2A
5. Let $x and $y be the selling prices of a glass of apple juice and a glass of orange juice
respectively. Accordingly,
⎩⎨⎧
=+
=+
)2(.......................11135)1(.......................14474
yxyx
(1) × 5, )3(........7203520 =+ yx
(2) × 4, )4(........4441220 =+ yx
2A
2A
2A
2A
2M
2M
2M
New Trend Mathematics (2nd Edition) S2A - Chapter Quiz - Chapter 4
8
© 2009 Chung Tai Educational Press. All rights reserved.
(3) − (4),
1227623
444720)1220()3520(
=
=
−=+−+
yyyxyx 2M
Substitute 12=y into (1),
15604144)12(74
=
=
=+
xx
x 2M
∴ The selling price of a glass of apple juice is $15, and
the selling price of a glass of orange juice is $12. 2A
6. Let the tens digit be x and the units digit be y, then the value of the original two-digit
number is yx +10 . Accordingly,
⎩⎨⎧
=+−+
=+
)2(.................9)10()10()1(........................................15
yxxyyx
From (2),
)3(........199991010
=−
=−
=−−+
xyxyyxxy
2M
(1) + (3),
8162
115)()(
=
=
+=−++
yyxyyx 2M
Substitute 8=y into (1),
7158
=
=+
xx 2M
∴ The original number is 78. 2A
7. (a) ⎩⎨⎧
=+
=−
)2(..............................745)1(..............................223
yxyx
(1) × 2, )3(...................446 =− yx 2M
(2) + (3),
11111
47)46()45(
=
=
+=−++
xxyxyx 2M
2A
2A
2M
2A
2A
2A
New Trend Mathematics (2nd Edition) S2A - Chapter Quiz - Chapter 4
9
© 2009 Chung Tai Educational Press. All rights reserved.
Substitute 1=x into (1),
211222)1(3
=
=
=−
y
yy 2M
∴ The solution of the simultaneous equations is 1=x , 21
=y . 2A
(b) Let bax −= and bay += , then the simultaneous equations
⎩⎨⎧
=++−
=+−−
7)(4)(52)(2)(3
babababa
can be written as
⎩⎨⎧
=+
=−
745223
yxyx
.
From (a), 1=x , 21
=y
∴
)5(.........................21
)4(..........................1
=+
=−
ba
ba
(4) + (5),
43232
=
=
a
a 2M
Substitute
43
=a into (4),
41
143
−=
=−
b
b 2M
∴ The solution of the simultaneous equations is
43
=a , 41
−=b . 2A
2A
2M
2M
2A
2A
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