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101
3
4.2 : 3, 4 56.1 : 1 26.2 : 16.3 : 16.4 : 1 26.5 : 1
1.
2. 3.
4.
3.1 (3 )3.2 (6 )3.3 (6 )
?
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102 .3
.3
+, , , ,
1) 5 6 7 3 24
2) 9 3 4 1 24
3) 1 2 3 5 24
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3 103
.3
33..11
:
1.
2.
/ : 1. 2. 3. 4. 5. 6.
: 1. 2. 3. 4. 5. 6.
M T
Series
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104 .3
.3
10 x y
x 1 2 3 4 5 6 7 8 9
y 9 8
(1, 9), (2, 8), .
x y
Y
0 1 2 3 4 5 6 7 8 9 X
1 5
x + y = 10 x + y = 10
x y
9
87
6
5
4
3
2
1
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3 105
.3
Y
0 1 2 3 4 5 6 7 8 9 X
x + 3y = 2, 2x y = 4 3x + 2y = 6
Ax + By + C = 0 (*)
x, y A, B, C A 0 B 0(x, y) (*)
Ax + By + C = 0
x 3y = 6 (1)
2x 6y = 8 (2)
(1) (2)
a, b, c, d, e f a, b c, d
ax + by = e
cx + dy = f
x y
a c x b d y
9
8
7
6
5
4
3
2
1
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106 .3
.3
(x, y) (x, y) x y
1 x + y = 6 (1)
2x y = 3 (2)
x x
y y
x + y = 6 2x y = 3
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3 107
.3
2 x + y = 2 (1)
2x + 2y = 4 (2)
x x
y y
x + y = 2 2x + 2y = 4
5 ..
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108 .3
.3
3 y x = 3 (1)
y = x + 3 (2)
x x
y y
y x = 3 y = x + 3
(1)(2)(3)
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3 109
.3
1. 1) x + 2y = 4, 2x + 3y = 7
x x
y y
2) y + x = -2, 2y + 2x = -4
x x
y y
3.1 :
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110 .3
.3
3) x 3y = 6, 2x 6y = 8
x x
y y
4) 2x + y = -3, 4x + 2y = -6
x x
y y
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3 111
.3
5) 2y x = 6, 2y = x 4
x x
y y
6) 2x 3y 14 = 0, 3x + 2y = 8
x x
y y
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112 .3
.3
2. 1)
2)
6y + 4x = -12
3y + 2x = -6
2x + y = 3
2x + y + 5 = 0
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3 113
.3
3)
4)
x + 2y = 4
2x - 3y = 1
x + y = 0 x 3 = 0
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114 .3
.3
5)
6)
x + 2y = 4y = x + 5
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3 115
.3
33..22
/ : 1. 2. 3. 4. 5. 6.
: 1. 2. 3. 4. 5. 6.
: 1. 2.
M T
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116 .3
.3
1 2
1) (
)2) 1) 3) 2)4) 3) 1)
1 x + y = 16 y x = 2 x + y = 16 (1)
y x = 2 (2)
(2) x y = 2 + x (3) y (3) (1)
x + (2 + x) = 16
2x + 2 = 16
2x = 16 2 =
2x
2 =
x =
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3 117
.3
x = 7 (3) y = 7 + 2 = 9
x y (1) (2) 7 + 9 = 16
9 7 = 2 (7, 9)
2 x y = 6 2x y = 4 x y = 6 (1)
2x y = 4 (2)
(1) y x = 6 + y (3) x (3) (2)
2(6 + y) y = 4
12 + 2y y = 4
12 + y = 4
y =
y =
y = -8 (3) x = 6 + =
x y (1) (2) = 16
= 4
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118 .3
.3
1. x + y = 20 x y = 4 ..
..
..
..
..
..
..
..
..
..
..
..
..
2. x + y = 12 2x y = 3 ..
..
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....
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..
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..
3.2 :
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3 119
.3
3. 2x + y = 6 3x + 4y = 4
..
..
..
..
..
..
..
..
..
..
..
..
..
..
4. x + 2y = 1 x 2y = 5 ..
..
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120 .3
.3
1) Ax + By = C A, B, C 2)
... 10 100 1,000,
3) 4) 5)
3 5x + 3y = 17 -5x + 2y = 3 5x + 3y = 17 (1)
-5x + 2y = 3 (2)
(1) + (2) (5x + 3y) + (-5x + 2y) = 17 + 3
5y = 20
=
y = =
=
=
=
=
x y (1) (2) =
=
(1) + (2) (1) (2) x
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3 121
.3
4 3x + 3y = 15 2x + 6y = 22
3x + 3y = 15 (1)
2x + 6y = 22 (2)
(1)2 6x + 6y = 30 (3)(3) (2)
(6x + 6y) (2x + 6y) = 30 22
=
=
=
=
=
=
=
x y (1) (2)
=
=
5 2x + 4y = 3 3x + 6y = 8 2x + 4y = 3 (1)
3x + 6y = 8 (2)
(1)3 6x + 12y = 9 (3)(2) 2 6x + 12y = 16 (4)(3) (4) (6x + 12y)
(6x + 12y) = 30 22
=
= ..
(1) 2 y
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122 .3
.3
6 x 2y = -3 -3x + 6y = 9
x 2y = -3 (1)
-3x + 6y = 9 (2)
(2) (-3) = (3)(3) (2) (1)(1) (2) (1) 2y = x + 3
=
7 -0.3x + 0.5y = -0.1 0.01x 0.4y = -0.8 -0.3x + 0.5y = -0.1
(1)
0.01x 0.4y = -0.8 (2)
(1)10 = (3)(2) x + 40y = -38 (4)
(4) 3 = (5)(3) + (5) =
=
=
=
=
=
=
=
x y (1) (2) =
=
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3 123
.3
8 12
x +2
3y = 1 3
4x
1
3y = 2
12x + 2
3y = 1 (1)
3
4x
1
3y = 2 (2)
(1) = = (3)
(2) = = (4)
(3) + (4) =
=
=
=
=
=
=
=
=
x y (1) (2)
=
=
... 2 3
... 4 3
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124 .3
.3
1. x + 3y = 7 -x + 4y = 7 ..
..
..
..
..
..
..
..
..
..
..
..
..
2. x 2y = 6 -x + 3y = -4 ..
..
..
..
....
..
..
..
..
..
..
..
3.3 :
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3 125
.3
3. x + 7y = 8 3x + 2y = 5
..
..
..
..
..
..
..
..
..
..
..
..
..
..
4. 3x y = 7 4x 3y 11 = 0 ..
..
..
..
..
..
..
..
..
..
..
..
..
..
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126 .3
.3
5. x + 2y 1 = 0 2x + 4y = 5
..
..
..
..
..
..
..
..
..
..
..
..
..
..
6. 4x 3y = 12 x = 34 y + 3
....
..
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..
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..
..
..
..
..
..
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3 127
.3
7. 0.2x + 0.3y = 0.1 0.03x 0.01y = 0.07
..
..
..
..
..
..
..
..
..
..
..
..
..
..
8. 35
x + 23
y = 14 34 x 13 y = 14
....
..
..
..
..
..
..
..
..
..
..
..
..
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128 .3
.3
9 2x = 5y + 1 24 7x = 3y 2x = 5y + 1 (1)
24 7x = 3y (2)
(1) x = (3)
x = (2) =
=
=
=
=
y = (3) =
=
=
x y (1) (2) =
=
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3 129
.3
1. 11x + 8y = -12 13x 6y = 83 ..
..
..
..
..
..
..
..
..
..
..
..
..
2. 2x + 3y = 1.6 3x 4y = 4.1 ..
..
..
..
....
..
..
..
..
..
..
..
3.4 :
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130 .3
.3
3. x + 7y = 8 3x + 2y = 5
..
..
..
..
..
..
..
..
..
..
..
..
..
..
4. 2x 3y = -9 3(x 1) = 5(y 4) + 2 ..
..
..
..
..
..
..
..
..
..
..
..
..
..
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3 131
.3
33..33
/ : 1. 2. 3. 4. 5. 6. :
1. 2. 3. 4. 5. 6.
: 1. 2.
M T
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132 .3
.3
5
1
2 345
1 43 23
x y 43
1
2(x + y) = 43 (1)
23 3y 2x = 23 (2)
(1) 2 = (3)
(3) 2 = (4)(2) + (4) . =
. =
. =
. =
. =
??
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3 133
.3
. =
.
.
2 78
24 x y
78 = (1)
24 = (2)
= (3)
. =
. =
. =
. =
. =
. =
. =
. =
...
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134 .3
.3
3 36
4
36
2x + 2y = 36 (1)
4 = (2)
(1) 2 = (3)(2) + (3) . =
. =
(3) (2) . =
. =
.
.
4 4 5.50 6 20 %
x 4x y 5.50y x + y 4x + 5.50y 6 20 %
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3 135
.3
120 100
6 1006
= 5120 5 5(x + y) 4x + 5.50y = 5(x + y)
4x + 5.50y = 5x + 5y
. =
. =
. =
. =
. =
.
3 6 3 .1 : 2
5 9,600 6% 8% 632
x 6%
y 8%9,600
x + y = 9,600 (1)
6% 6100
x
8% 8100 x
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136 .3
.3
632 = 632 (2)
(2)100 = (3)(1) 6x + 6y = 57,600 (4)(3) (4) . =
. =
(1)
. =
. =
6% 8% .6% 8% .
6%
8%
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3 137
.3
1. 16
....
..
..
..
..
..
..
..
..
..
..
2. 2 3 35 3 6 60
....
..
....
..
..
..
..
..
..
..
3.5 :
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138 .3
.3
3. 628 6
....
..
..
..
..
..
..
..
..
..
..
4. 12 14
15 20 %
....
..
..
..
..
..
..
..
..
..
..
..
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3 139
.3
5. 880,000 132,600 14% 16%
....
..
..
..
..
..
..
..
..
..
..
6. 10 1 200 920
....
..
..
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..
..
..
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..
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140 .3
.3
