Морозов А.В. Домашняя работа по алгебре за 7 класс
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151
в)
{
6
35 2
xy
xy
+=
−
=
, y = 6 – x, 3x – 5(6 – x) = 2, 3x – 30 + 5x = 2,
8x = 32, x = 4, y = 6 – 4 = 2;
Ответ: (4; 2).
г)
{
411
6213
xy
xy
−=
−
=
, y = 4y – 11, 6x – 2(4x – 11) = 13,
6x – 8x + 22 = 13, 2x = 9, x = 4,5, y = 4 ⋅ 4,5 – 11 = 7.
Ответ: (4,5; 7).
д)
{
20
215 1
yx
xy
−=
−
=−
, y = x + 20, 2x – 15(x + 20) = –1,
2x – 15x – 300 = –1, 13x = –299, x = –23, y = –23 + 20 = –3.
Ответ: (–23; –3).
е)
{
25 4
32 30
x
y
xy
−
=−
−=
, x = 4y + 25, 3(4y + 25) – 2y = 30,
12y + 75 – 2y = 30, 10y = –45, y = –4,5, x = 4 ⋅ (–4,5) + 25 = 7.
Ответ: (7; –4,5).
№1134.
а)
{
212
7231
xy
xy
+=
−
=
, y = 12 – 2x, 7x – 2(12 – 2x) = 31,
7x – 24 + 4x = 31, 11x = 55, x = 5, y = 12 – 2 ⋅ 5 = 2.
Ответ: (5; 2).
б)
{
24
71
yx
xy
−=
−
=
, y = 2x + 4, 7x – (2x + 4) = 1,
7x – 2x – 4 = 1, 5x = 5, x = 1, y = 2 ⋅ 1 + 4 = 6.
Ответ: (1; 6).
в)
{
84
2212
yx
xy
−=
−
=
, x = 8y – 4, 2(8y – 4) – 21y= 2, 16y – 8 – 21y = 2,
5y = –10, y = –2, x = 8 ⋅ (–2) – 4= –20.
Ответ: (–20; –2).
г)
{
205
3513
x
y,
xy
=+
−=
, y = 2x – 0,5, 3x – 5 ⋅ (2x – 0,5) = 13,
3x – 10x + 2,5 = 13, 7x –10,5, x = –1,5, y = 2 ⋅ (–1,5) – 0,5 = –3,5.
Ответ: (–1,5; –3,5).
№1135.
а)
{
250
8157
uv
uv
+=
−+ =
,
{
25
8157
u,v
uv
=−
−+ =
,
(
)
825 157,v v
−
⋅− + = ,
35 7v = ,
02v,=
, u = –2,5 ⋅ 0,2 = –0,5.
Ответ: (–0,5; 0,2).
б)
{
530
3429
pq
pq
−=
+=
,
06p,q=
,
306 4 2,q q q
⋅
+=
,
58 29,q
=
,
5q
=
, p=3.
Ответ: (3; 5).
152
в)
{
4314
5325
uv
uv
+
=
−=
, 3 14 4vu=−, 5 4 14 25uu
+
−=, 9 39u
=
,
1
4
3
u =
,
14 16 4 1
1
339 9
u =−−=−
.
Ответ:
11
41
39
;
⎛⎞
−
⎜⎟
⎝⎠
.
г)
{
10 7 2
2225
pq
pq
+
=−
−=
, 25 11p,q=+, 25 110 7 2qq
+
+=−,
32 112q =− , q = –3,5, p = 2,25.
Ответ: (2,25; –3,5).
№1136.
а)
{
34 0
231
xy
xy
+
=
+
=
,
05 15
x
,,y=−
,
15 45 4 0,,yy
−
+=
,
15 05,,y
=
,
y = 3, x = 0,5 – 1,5 ⋅ 3 = –4.
Ответ: (–4; 3).
б)
{
720
4910
xy
yx
+
=
+
=
,
27yx=−
, 14 9 10xx
−
+=, 510x
−
= , x=–2, y=7.
Ответ: (–2; 7).
в)
{
56 20
9225
xy
yx
+
=−
+=
, 12 5 4 5
x
,,y=− , 5125 5 45 6 20,,yy
⋅
−⋅ + =− ,
16 5 82 5,y ,−=−, y = 5, x = 12,5 – 4,5 ⋅ 5 = –10.
Ответ: (–10; 5).
г)
{
318
11 3 11
xy
yx
+=
−
=−
, 3 8 1
x
y=−, 11 8 1 11yy
−
+=− ,
312y
=
−
, y = –4.
Ответ: (–11; –4).
№1137.
а)
{
74 23
810 19
xy
xy
+=
−
=
, 211535y,,x=− , 857517519x, ,
−
+=,
25 5 76 5,x ,
=
, x = 3, y = 0,5.
Ответ: A(3; 0,5).
б)
{
11 6 2
85 3
xy
xy
−
=
−+ =
,
06 16y, ,x=+
,
11 3 6 9 6 2x, ,x
−
−=
,
14 56,x ,= , x = 4, y = 7.
Ответ: B(4; 7).
№1138.
а)
{
5416
26
xy
xy
−
=
−=
, x = 2y + 6, 5(2y + 6) – 4y = 16,
10y + 30 – 4y = 16, 6y = –14, y = –
71
2
33
=−
, x = –2 ⋅
71
61
33
+=
.
Ответ:
11
12
33
;
⎛⎞
−
⎜⎟
⎝⎠
.
153
б)
{
20 15 100
36
xy
xy
−=
−=
, y = 3x – 6, 20x – 15(3x – 6) = 100,
4x – 9x + 18 = 20, 5x = –2, x = –0,4, y = 3 ⋅ (–0,4) – 6 = –7,2.
Ответ: (–0,4; –7,2).
№1139.
а)
{
3( 5) 1 6 2
3( ) 7 4
x
x
xy y
−
−= −
−
−=−
,
{
31662
337 4
x
x
xyy
−=−
−
−=−
,
{
522
310 4
x
xy
=
−
=−
,
x = 4,4, 3 ⋅ 4.4 – 10y = –4, 10y = 17,2, y = 1,72.
Ответ: (4,4; 1,72).
б)
{
6( ) 1
7( 4) ( 2) 0
xy y
yy
+−=−
+
−+=
{
65 1
728 20
xy
yy
+=−
+
−−=
{
65 1
626
xy
y
+
=−
=−
y = –
13 1
4
33
=
−
, 6x – 5 ⋅
13
3
= –1, 6x =
62
3
, x =
5
3
9
.
Ответ:
51
34
93
;
⎛⎞
−
⎜⎟
⎝⎠
.
№1140.
а)
{
2(3 2 ) 1 7
12( ) 15 7 12
xy x
x
yxy
−+=
+−=+
{
6417
12 12 15 7 12
xy x
x
yxy
−+=
+−=+
{
410
515
xy
x
−
−+=
=
3x = , 05y,=− .
Ответ: (3; –0,5).
б)
{
3( ) 7 12
6( 2 ) 1 45
x
yxy
yx x
+
−= +
−−=−
{
33712
612145
x
yxy
yx x
+
−= +
−−=−
{
927
33 6 1
xy
xy
−
+=
+
=
y = 4,5x + 3,5, 33x + 6(4,5x + 3,5) = 1, 60x = –20, x = –
1
3
,
y = –4,5 ⋅
1
3
+ 3,5 = 2.
Ответ:
1
2
3
;
⎛⎞
−
⎜⎟
⎝⎠
.
в)
{
5( 2 ) 3 3 5
4( 3 ) 50 33
xy x
x
yy
+
−= +
−−=−
{
510 335
412 50 33
xy x
x
yy
+
−= +
−−=−
{
210 8
42150
xy
xy
+
=
+
=
x = 4 – 5y, 4(4 – 5y) + 21y = 50, 16 – 20y + 21y = 50, y = 34,
x = 4 – 5 ⋅ 34 = –166.
Ответ: (–166; 34).
г)
{
415(3)6
3( 6 ) 4 9 19
xxy
xy y
+= − −
+
+= +
{
41515 6
318 4919
xxy
xy y
+= − −
+
+= +
{
15 7
3915
xy
xy
−
+=−
+=
x = 15y + 7, (15y + 7) + 3y = 5, 18y = –2, y = –
1
9
, x = –15 ⋅
1
9
⎛⎞
−
⎜⎟
⎝⎠
+ 7 =
1
5
3
.
Ответ:
11
5
39
;
⎛⎞
−
⎜⎟
⎝⎠
.
154
№1141.
а)
{
58(3)712
93(9)1146
yxy x
xxy y
+− =−
+
−=+
{
5824712
12 27 11 46
yx y x
xyy
+
−=−
−=+
{
19 12
12 38 46
xy
xy
−=−
−
=
x = 19y – 12, 12(19y – 12) – 38y = 46, 190y = 190, y = 1,
x = 19 ⋅ 1 – 12 = 7. Ответ: (7; 1).
б)
{
2( ) 16 3( 7)
6(5)8(1)
ab b
aa b
−−+= +
−
−=−−+
{
2216321
558 1
ab b
ab
−
++=+
+=−−−
{
24
514
ab
ab
−
−=
+
=−
b = –5a – 14, –2a – (–5a – 14) = 5, 3a = 5 – 14, a=–3, b = –5 ⋅ (–3) – 14 = 1.
Ответ: (–3; 1).
№1142.
а)
4
32
2
24
xy
xy
⎧
−=−
⎪
⎨
⎪
+=−
⎩
{
23 24
28
xy
xy
−=−
−=−
y = 2x + 8,
2x – 3(2x + 8) = –24, –4x = 0, x = 0, y = 8. Ответ: (0; 8).
б)
26
6
337
2
a
b
b
a
⎧
−=
⎪
⎨
⎪
−+=−
⎩
{
12 36
674
ab
ab
−=
−+=−
a = 12b + 36, –6(12b + 36) + b = –74,
–71b = 142, b = –2, a = 12 ⋅ (–2) + 36 = 12. Ответ: (12; –2).
в)
2
1
53
7
4
10 6
mn
mn
⎧
+
=
⎪
⎨
⎪
−
=
⎩
{
65 15
3 35 120
mn
mn
+−=
−=
n = 3 – 1,2m, 3m – 35(3 – 1,2m) = 120,
45m = 120 + 105, m = 5, n = 3 – 1,2 ⋅ 5 = –3. Ответ: (5; –3).
г)
3
74
5
2
3
5
y
x
y
x
⎧
−
=−
⎪
⎨
⎪
+=−
⎩
{
35 3 20
52 15
xy
xy
−=−
+=−
y = –2,5x – 7,5,
35x – 3(–2,5x – 7,5) = –20, 42,5x = –42,5, x = –1, y = –2.5 ⋅ (–1) – 7,5 = –5.
Ответ: (–1; –5).
№1143.
а)
6
45
0
15 12
yx
xy
⎧
−=
⎪
⎨
⎪
+
=
⎩
{
5 4 120
430
yx
xy
−=
+=
4x = –3y, 5y – (–3y) = 120,
8y = 120, y = 15, 4x = –45, x = –10,8. Ответ: (–10,8; 15).
б)
6
23
515
2
12
10 3
xy
,
xy
,
⎧
+=
⎪
⎨
⎪
−=
⎩
{
18 34 5
320 36
x
y,
xy
+=
−=
y = 34,5 – 18x, 3x – 20(34,5 – 18x) = 36,
363x = 726, x = 2, y = 34,5 – 18 ⋅ 2 = –1,5. Ответ: (2; –1,5).
155
№1144.
а) (2x–3y)
2
+(2x+3y)
2
= 4x
2
– 12xy + 9y
2
+ 4x
2
+ 12xy + 9y
2
= 8x
2
+ 18y
2
;
б) (2x + 3y)
2
– (2x – 3y)
2
= 4x
2
+ 12xy + 9y
2
– (4x
2
– 12xy + 9y
2
) =
= 4x
2
+ 12xy + 9y
2
– 4x
2
+ 12xy – 9y
2
= 24xy;
в)
2
22
2
2(2)2
24 4 4 16
x
yxxyy
xy
⎛⎞
⎛⎞
++−= ++
⎜⎟
⎜⎟
⎝⎠
⎝⎠
+ 4x
2
– 4xy + y
2
=
=
22
228
x
xy y
++
+ 4x
2
– 4xy + y
2
=
22
111
431
428
x
xy y−+
;
г)
2
22
2
2
3(3)3
39 9 27 81
x
yxxyy
xy
⎛⎞
⎛⎞
+−−= ++
⎜⎟
⎜⎟
⎝⎠
⎝⎠
– (9x
2
– 6xy + y
2
) =
=
22
2
3927
x
xy y
++
– 9x
2
+ 6xy – y
2
=
22
2226
86
3927
x
xy y−+ −
;
д) (x + 2)
3
+(x – 2)
3
= (x + 2 + x – 2)((x + 2)
2
– (x + 2)(x – 2) + (x – 2)
2
) =
= 2x(x
2
+ 4x + 4 – x
2
+ 4 + x
2
– 4x + 4) = 2x(x
2
+ 8);
е) (x + 2)
3
–(x – 2)
3
= (x + 2 – x + 2)((x + 2)
2
+ (x + 2)(x – 2) + (x – 2)
2
) =
= 4(x
2
+ 4x + 4 + x
2
– 4 + x
2
– 4x + 4) = 4(3x
2
+ 4).
№1145.
а) x
5
+ 4a
2
x
3
– 4ax
4
= x
3
(x
2
– 4ax + 4a
2
) = x
3
(x – 2a)
2
= x
3
(x – 2a)(x – 2a);
б) 4a
6
–12a
5
b+9a
4
b
2
=a
4
(4a
2
–12ab+9b
2
)=a
4
(2a–3b)
2
=a
4
(2a–3b)(2a – 3b);
в)
4
1
y
4
+
9
1
y
2
c
2
–
3
1
y
3
c = y
2
2
22
22
77
439 23 2323
y ycc yc c c
yy
⎛⎞
⎛⎞ ⎛⎞⎛⎞
−+ = − = − −
⎜⎟
⎜⎟ ⎜⎟⎜⎟
⎝⎠ ⎝⎠⎝⎠
⎝⎠
;
г)
9
4
b
5
+ 4b
3
c + 9bc
2
= b
2
42 2 2
42
49 3
93
bbccbbc
⎛⎞⎛⎞
+
+= +=
⎜⎟⎜⎟
⎝⎠⎝⎠
=
22
22
33
33
bb c b c
⎛⎞⎛⎞
++
⎜⎟⎜⎟
⎝⎠⎝⎠
;
д)
4
1
x
2
– y
2
+
22
1111
2222
x
yxyxyxy
⎛⎞⎛⎞⎛⎞⎛⎞
+= − ++ +
⎜⎟⎜⎟⎜⎟⎜⎟
⎝⎠⎝⎠⎝⎠⎝⎠
=
=
11 1 1
22 2 2
x
yxy xyxxy
⎛⎞⎛⎞⎛⎞
−+ + + = +
⎜⎟⎜⎟⎜⎟
⎝⎠⎝⎠⎝⎠
;
е)
4
1
x
2
– y
2
–
22
1111
2222
x
yxyxyxy
⎛⎞⎛⎞⎛⎞⎛⎞
−= − +− −
⎜⎟⎜⎟⎜⎟⎜⎟
⎝⎠⎝⎠⎝⎠⎝⎠
=
=
11 1 1
2
22 2 2
x
yxy xy yxy
⎛ ⎞⎛⎞⎛⎞
+
−+ −= −
⎜ ⎟⎜⎟⎜⎟
⎝ ⎠⎝⎠⎝⎠
.
№1146.
y = x
2
– 4x + 5 = (x
2
– 4x + 4) + 1 = (x – 2)
2
+ 1 > 0,
т.е. у всех точек графика y > 0, т.е. они лежат в верхней полуплоскости.
156
43. Способ сложения
№1147.
а)
{
21115
10 11 9
xy
xy
+
=
−
=
{
12 24
10 11 9
x
xy
=
−=
{
2
10 11 9
x
xy
=
−
=
{
2
1
x
y
=
=
Ответ: (2; 1).
б)
{
817 4
815 4
xy
xy
−=
−+ =
{
28
815 4
y
xy
−=
−+ =
{
4
815(4)4
y
x
=−
−
+⋅−=
{
4
8
y
x
=
−
=
−
Ответ: (–8; –4).
в)
{
47 30
45 90
xy
xy
−=
−=
{
47 30
260
xy
y
−=
=
{
30
4 7 30 30
y
x
=
−⋅ =
{
30
60
y
x
=
=
Ответ: (60; 30).
г)
{
13 8 28
11 8 24
xy
xy
−
=
−=
{
24
11 8 24
x
xy
=
−=
{
2
11 2 8 24
x
y
=
⋅− =
{
2
025
x
y,
=
=−
Ответ: (2; –0,25).
№1148.
а)
{
617
5613
xy
xy
−=
+
=
{
630
5613
x
xy
=
+=
{
5
25 6 13
x
y
=
+
=
{
5
2
x
y
=
=
−
Ответ: (5; –2).
б)
{
47 12
4312
xy
xy
−
=−
−+ =
{
40
4312
y
xy
−=
−+ =
{
0
43012
y
x
=
−
+⋅=
{
0
3
y
x
=
=
−
Ответ: (–3; 0).
в)
{
32 5
52 45
xy
xy
+=
−+ =
{
840
32 5
x
xy
=−
+=
{
5
3( 5) 2 5
x
y
=−
⋅
−+ =
{
5
10
x
y
=
−
=
Ответ: (–5; 10).
г)
{
94 13
92 20
xy
xy
−
=−
−
=−
–2y = 7, y = –3,5,
20 2 27
3
99 9
xy
=
− + =− =−
.
Ответ: (–3; –3,5).
№1149.
а)
{
40 3 10
20 7 5
xy
xy
+
=
−
=
{
40 3 10
40 14 10
xy
xy
+=
−=
{
17 0
20 7 5
y
xy
=
−
=
{
0
025
y
x
,
=
=
Ответ: (0,25; 0).
б)
{
521
15 3 3
xy
xy
−=
−
=−
{
521
51
xy
xy
−=
−=−
{
2
51
y
xy
−=
−
=−
{
2
06
y
x
,
=
−
=−
Ответ: (–0,6; –2).
в)
{
33 42 10
914 4
ab
ab
+
=
+=
{
33 42 10
27 42 12
ab
ab
+=
+=
{
62
14 4 9
a
ba
=−
=−
1
3
1
2
a
b
⎧
=
−
⎪
⎨
⎪
=
⎩
Ответ:
11
32
;
⎛⎞
−
⎜⎟
⎝⎠
.
157
г)
{
13 12 14
11 4 18
xy
x
y
−
=
−=
{
39 36 42
22 36 8
xy
xy
−=
−=
{
17 34
18 11 4
x
yx
=
=
−
{
2
1
x
y
=
=
Ответ: (2; 1).
д)
{
10 9 8
21 15 0 5
xy
yx,
−=
+=
{
30 27 24
42 30 1
xy
yx
−=
+=
{
69 23
42 30 1
y
yx
=−
+
=
1
3
1
2
y
x
⎧
=
−
⎪
⎨
⎪
=
⎩
Ответ:
11
23
;
⎛⎞
−
⎜⎟
⎝⎠
.
е)
{
98 2
5411
yx
xy
+
=−
=
−−
{
45 40 10
32 40 88
yx
yx
+=−
+=−
{
13 78
5411
y
xy
=
=
−−
{
6
7
y
x
=
=
−
Ответ: (–7; 6).
№1150.
а)
{
12 7 2
45 6
xy
xy
−
=
−
=
{
816
465
y
x
y
=−
=+
{
2
1
y
x
=
−
=
−
Ответ: (–1; –2).
б)
{
721
17 6 9
uv
uv
+=
+
=−
{
21 6 3
17 6 9
uv
uv
+=
+=−
{
412
217
u
vu
=
=−
{
3
10
u
v
=
=
−
Ответ: (3; –10).
в)
{
6251
516 4
xy
xy
=
+
−
=−
{
30 125 5
30 96 24
xy
xy
−=
−=−
{
29 29
516 4
y
xy
−=
=
−
{
1
4
y
x
=
−
=
−
Ответ: (–4; –1).
г)
{
4790
5620
ba
ab
+
=
−=
{
21 12 270
10 12 40
ab
ab
+=
−=
{
31 310
4907
a
ba
=
=−
{
10
5
a
b
=
=
Ответ: (10; 5).
№1151.
а)
{
075 20 95
032 25 7
,x y
,x y
+=
−=
{
3 75 100 475
1 28 100 28
,x y
,x y
+=
−=
{
5 03 503
25 0 32 7
,x
y,x
=
=
−
{
100
1
x
y
=
=
Ответ: (100; 1).
б)
{
05 06 0
04 17 109
,u ,v
,u ,v ,
−=
+=
{
2240
285545
u,v
u,v ,
−=
+=
{
10 9 54 5
12
,v ,
u,
=
=
{
5
6
v
u
=
=
Ответ: (6; 5).
в)
{
10 4 6 3
4326
x
,y
y, x
=+
+=
{
40 12 18 4
12 18 9 6
x
y,
yx ,
−=
−=−
{
22 8 8
15 08
x,
y,x,
=
=−
{
04
02
x
,
y,
=
=−
Ответ: (0,4; –0,2).
г)
{
310 010
15 4 2 7 0
ba,
ab,
−+ − =
+
−=
{
12 40 0 4 0
45 12 8 1 0
ba,
ab,
−+ −=
+−=
{
85 8 5
42715
a,
b, a
=
=−
{
01
03
a,
b,
=
=
Ответ: (0,1; 0,3).
№1152.
а)
{
55
10 19
kb
kb
+=
−+=−
{
15 24
10 19
k
bk
=
=−
{
16
3
k,
b
=
=
−
y = 1,6x – 3;
158
б)
{
41
35
kb
kb
+
=
+
=−
{
6
53
k
bk
=
=− −
{
6
23
k
b
=
=
−
y = 6x – 23;
в)
{
81
417
kb
kb
+
=−
−+=
{
12 18
14 17
k
bk
=−
=+
{
15
11
k,
b
=−
=
y = –1,5x + 11;
г)
{
19 31
9
kb
kb
−+=
+=−
{
20 40
9
k
bk
−=
=− −
{
2
7
k
b
=
−
=
−
y = –2x – 7.
№1153.
y = kx + b
(0; 11) ∈ графику, значит b=11, (–5; 0) ∈ графику, значит –5k + b=0,
–5k + 11 = 0, k = 2,2, у = 2,2х + 11.
№1154.
y = kx + b
(–1; 3) ∈ графику, значит –k + b = 3,
(2; –1) ∈ графику, значит 2k + b = –1,
{
3
21
kb
kb
−+ =
+=−
,
{
34
21
k
bk
−=
=− −
, тогда k = –
4
3
, b =
5
3
, y = –
15
1
33
x
+
№1155.
y = kx + b
{
40
011
kb
kb
⋅+=
⋅+=
,
{
11
275
b
k,
=
=−
, значит, y = –2,75x + 11.
№1156.
График y = kx + b пересекается с Оy в (0; –1) ⇒ b =–1, т.к. если x=–1, то y =
1, имеем: k⋅(–1)+b=1 ⇒ –k – 1 = 1, k = –2. Значит y = –2x – 1.
№1157.
а)
{
5( 2 ) 3 5
4( 3 ) 50
xy x
yxy
+
−=+
+−=
{
510 3 5
412 50
xy x
yx y
+
−=+
+− =
{
410 8
411 50
xy
xy
+
=
−
=
{
21 42
225
y
x
,y
=−
=−
{
2
7
y
x
=−
=
Ответ: (7; –2).
б)
{
25( 3 ) 3 3 05
3( 6 ) 4 9 19
,x y x ,
xy y
−−=−+
++=+
{
515 6 61
318 4919
xy x
xy y
−
−=− +
+
+= +
{
11 15 7
3915
xy
xy
−=
+=
{
53
55 33 15 7
xy
yy
=−
−−=
{
1
2
y
x
=
=
Ответ: (2; 1).
№1158.
а)
11
20
34
511
xy
xy
⎧
⎪
+
−=
⎨
⎪
−=
⎩
{
43 24
511
xy
yx
+
=
=−
4x + 15x – 33 = 24, 19x = 57, x = 3, y = 11 – 5 ⋅ 3 = –4.
Ответ: (3; –4).
159
б)
11
0
56
542
mn
mn
⎧
⎪
−
=
⎨
⎪
−
=
⎩
{
650
542
mn
mn
−=
−=
n = 1,2m, 5m – 4 ⋅ 1,2m = 2;
0,2m = 2, m = 10; n = 1,2 ⋅ 10 = 12.
Ответ: (10; 12).
в)
05 02 7
11
0
310
,x ,y
xy
+
=
⎧
⎪
⎨
−=
⎪
⎩
x = 0,3y
0,5 ⋅ 0,3y + 0,2y = 7, 0,35y = 7, y= 20, x = 0,3 ⋅ 20 = 12
Ответ: (12; 20).
г)
11
3
63
02 01 39
uv
,u ,v ,
⎧
⎪
−=−
⎨
⎪
+=
⎩
u = 2v – 18, 0,2(2v – 18) + 0,1v = 3,9,
0,5v = 7,5, v = 15, u = 2 ⋅ 15 – 18 = 12.
Ответ: (12; 15).
№1159.
а)
50
34
210
xy
xy
⎧
⎪
+−=
⎨
⎪
−=
⎩
{
4360
210
xy
yx
+=
=−
4x+3(2x – 10) = 60, 4x + 6x – 30 = 60, 10x = 90, x = 9, y = 2⋅9–10 = 8.
Ответ: (9; 8).
б)
27 4
0
66
xy
xy
−
=
⎧
⎪
⎨
−=
⎪
⎩
y = x, 5x = –4, x = –0,8, y = –0,8.
Ответ: (–0,8; –0,8).
в)
2
0
32
3( 1) 9 1
xy
x
y
⎧
⎪
−=
⎨
⎪
−
−=−
⎩
{
43 0
3391
xy
x
y
−=
−
−=−
x = 0,75y, 3 ⋅ 0,75y + y = 13, 3,25y = 13, y = 4, x = 0,75 ⋅ 4 = 3.
Ответ: (3; 4).
г)
55
66
22
3
33
x
y
x
y
⎧
−=−
⎪
⎨
⎪
+
=−
⎩
{
15 18 15
418 4
xy
xy
−=−
+=−
19x = –19, x = –1, 4 ⋅ (–1) + 18y = –4, 18y = 0, y = 0.
Ответ: (–1; 0).
№1160.
а)
11
412
312
6 5 150
xy|
xy
⎧
⎪
−
=⋅
⎨
⎪
+=
⎩
{
448
6 5 150
xy
xy
−=
+=
y = 4x – 48,
6x + 5(4x – 48) = 150, 26x = 390, x = 15, y = 4 ⋅ 15 – 48 = 12.
Ответ: (12; 15).
160
б)
11
324
38
79 2
vu|
uv
⎧
⎪
−=⋅
⎨
⎪
+=−
⎩
{
83 72
79 2
vu
uv
−=
+
=−
v + 10u = –74,
8(–74 – 10u) – 3u = 72, –83u = 664, u = –8, v = 80 – 74 = 6.
Ответ: (–8; 6).
в)
1
46
23 12
xy
xy
⎧
⎪
+=
⎨
⎪
+
=−
⎩
{
3212
23 12
xy
xy
+=
+=−
{
55 0
3212
xy
xx
+
=
−
=
,
{
12
yx
x
=
−
=
y = –12.
Ответ: (12; –12).
г)
45100
1
0
533
ab
ab
−
−=
⎧
⎪
⎨
−+=
⎪
⎩
{
4510
35 5
ab
ab
−
=
−
=−
a = 15,
4 ⋅ 15 – 5b = 10, 5b = 50, b = 10.
Ответ: (15; 10).
№1161.
а)
{
21
63 2
xy
xy
−=
−+ =
{
63 3
63 2
xy
xy
−=
−+ =
{
00 5
21
xy
xy
⋅
+⋅=
−=
Решений нет.
б)
{
52 73
15 6 21
x
y|
xy
−+ =⋅
−=−
{
15 6 21
15 6 21
xy
xy
−+=
−
=−
{
00 0
15 6 21
xy
xy
⋅
+⋅=
−
=−
Бесконечно много решений вида.
№1162.
а) 15a
2
– 15b
2
= 15(a
2
– b
2
) = 15(a – b)(a + b);
б) 29a
2
+ 29b
2
+ 58ab = 29(a
2
+ b
2
+ 2ab) = 29(a + b)
2
= 29(a+b)(a + b);
в) 10a
3
+ 10b
3
= 10(a
3
+ b
3
) = 10(a + b)(a
2
–ab + b
2
);
г) 18a
3
– 18b
3
= 18(a
3
– b
3
) = 10(a – b)(a
2
+ ab + b
2
);
д) 47a
6
– 47b
6
= 47(a
6
– b
6
) = 47(a
3
– b
3
)(a
3
+ b
3
) =
= 47(a – b)(a
2
+ ab+ b
2
)(a + b)(a
2
– ab + b
2
);
е) 51a
6
+ 51b
6
= 51(a
6
+ b
6
) = 51(a
2
+ b
2
)(a
4
– a
2
b
2
+ b
4
).
№1163.
а) 2x(8x – 1) – (4x + 1)
2
= 16x
2
– 2x – (16x
2
+ 8x + 1) =
= 16x
2
– 2x – 16x
2
– 8x – 1 = –10x – 1;
б) 4(3y – 1)
2
– 18y(2y – 1) = 4(9y
2
– 6y + 1) – 36y
2
+ 18y =
= 36y
2
– 24y + 4 – 36y
2
+ 18y = –6y + 4.
№1164.
(1 + a)
3
≈ 1 + 3a;
а) 1,1
3
= (1 + 0,1)
3
≈ 1 + 3 ⋅ 0,1 = 1 + 0,3 = 1,3;
1,1
3
= 1,331, значит погрешность: |1,331 – 1,3| = 0,031;
б) 0,9
3
= (1 – 0,1)
3
≈ 1 – 3 ⋅ 0,1 = 1 – 0,3 = 0,7,
0,9
3
= 0,729, тогда погрешность: |0,729 – 0,7| = 0,029.