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{"id":44329,"date":"2019-10-15T15:04:49","date_gmt":"2019-10-15T08:04:49","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=44329"},"modified":"2019-10-15T15:04:53","modified_gmt":"2019-10-15T08:04:53","slug":"giai-toan-10-chuong-3-phuong-trinh-he-phuong-trinh-bai-3-phuong-trinh-va-he-phuong-trinh-bac-nhat-nhieu-an","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/giai-toan-10-chuong-3-phuong-trinh-he-phuong-trinh-bai-3-phuong-trinh-va-he-phuong-trinh-bac-nhat-nhieu-an\/","title":{"rendered":"[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 3: Ph\u01b0\u01a1ng tr\u00ecnh. H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh\/ B\u00e0i 3: Ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t nhi\u1ec1u \u1ea9n"},"content":{"rendered":"\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 63<\/strong>: C\u1eb7p (1; -2) c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 7 kh\u00f4ng ? Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 c\u00f2n c\u00f3 nh\u1eefng nghi\u1ec7m kh\u00e1c n\u1eefa kh\u00f4ng ?<\/ins><\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

Ta c\u00f3: 3.1-2.(-2) = 7 \u21d2 C\u1eb7p (1; -2) l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 7<\/p>\n\n\n\n

C\u00e1c nghi\u00eam kh\u00e1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 l\u00e0: (3; 1); (-1; -5)<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 64<\/strong>: H\u00e3y bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 6.<\/ins><\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

3x \u2013 2y = 6 \u21d4 y = 3\/2x – 3<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 6 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 3\/2x-3<\/ins><\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 64<\/strong>: a) C\u00f3 m\u1ea5y c\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

b) D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1 \u0111\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

C\u00f3 nh\u1eadn x\u00e9t v\u1ec1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y ?<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

a) C\u00f3 2 c\u00e1ch l\u00e0 c\u1ed9ng \u0111\u1ea1i s\u1ed1 v\u00e0 th\u1ebf<\/p>\n\n\n\n

b) <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u21d2 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m do ph\u01b0\u01a1ng tr\u00ecnh 0x + 0y = 9 v\u00f4 nghi\u1ec7m.<\/p>\n\n\n\n

Nh\u1eadn x\u00e9t: H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean v\u00f4 nghi\u1ec7m.<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 65<\/strong>: H\u00e3y gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (5).<\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t <\/p>\n\n\n\n

B\u00e0i 1 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

T\u1ea1i sao kh\u00f4ng c\u1ea7n gi\u1ea3i ta c\u0169ng k\u1ebft lu\u1eadn \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y v\u00f4 nghi\u1ec7m.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n

Ta c\u00f3:<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

Kh\u00f4ng t\u1ed3n t\u1ea1i c\u1eb7p nghi\u1ec7m (x ; y) n\u00e0o th\u1ecfa m\u00e3n h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean n\u00ean h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho v\u00f4 nghi\u1ec7m.<\/p>\n\n\n\n

B\u00e0i 2 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Gi\u1ea3i c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

C\u00e1ch 1: C\u1ed9ng \u0111\u1ea1i s\u1ed1.<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

a) \n (Nh\u00e2n c\u1ea3 hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai v\u1edbi 2) <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\n (L\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai tr\u1eeb \u0111i ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t). <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n<\/p>\n\n\n\n

C\u00e1ch 2: S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf.<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

T\u1eeb (2) suy ra x = 3 \u2013 2y, th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1) ta \u0111\u01b0\u1ee3c: <\/p>\n\n\n\n

2.(3 \u2013 2y) \u2013 3y = 1<\/p>\n\n\n\n

\u21d4 6 \u2013 4y \u2013 3y = 1<\/p>\n\n\n\n

\u21d4 7y = 5 <\/p>\n\n\n\n

\u21d4 y = 5\/7. <\/p>\n\n\n\n

Thay y = 5\/7 v\u00e0o x = 3 \u2013 2y ta \u0111\u01b0\u1ee3c : x = 3 \u2013 2.5\/7 = 11\/7. <\/p>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m (x ; y) = (11\/7 ; 5\/7). <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

T\u1eeb (2) r\u00fat ra \u0111\u01b0\u1ee3c y = 2x \u2013 1, th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1) ta \u0111\u01b0\u1ee3c <\/p>\n\n\n\n

3x + 4.(2x \u2013 1) = 5<\/p>\n\n\n\n

\u21d4 3x + 8x \u2013 4 = 5<\/p>\n\n\n\n

\u21d4 11x = 9 <\/p>\n\n\n\n

\u21d4 x = 9\/11<\/p>\n\n\n\n

Thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y = 2x \u2013 1 ta \u0111\u01b0\u1ee3c y = 2.9\/11 \u2013 1 = 7\/11. <\/p>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m (x; y) = (9\/11; 7\/11)<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

Thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh \n ta t\u00ecm \u0111\u01b0\u1ee3c \n\n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n\n\n<\/p>\n\n\n\n

T\u1eeb (1) r\u00fat ra 2y = 3x \u2013 5, thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (2) ta \u0111\u01b0\u1ee3c: \n<\/p>\n\n\n\n

5x + 2.(3x \u2013 5) = 12\n<\/p>\n\n\n\n

\u21d4 5x + 6x \u2013 10 = 12\n<\/p>\n\n\n\n

\u21d4 11x = 22\n<\/p>\n\n\n\n

\u21d4 x = 2. \n<\/p>\n\n\n\n

Thay x = 2 v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh 2y = 3x \u2013 5 ta \u0111\u01b0\u1ee3c 2y = 1 \u21d4 y = 1\/2. \n<\/p>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m (x ; y) = (2 ; 1\/2)\n<\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

C\u00f3 hai c\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 th\u1ebf ho\u1eb7c c\u1ed9ng \u0111\u1ea1i s\u1ed1. \u2003<\/p>\n\n\n\n

B\u00e0i 3 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Hai b\u1ea1n \nV\u00e2n v\u00e0 Lan \u0111\u1ebfn c\u1eeda h\u00e0ng mua tr\u00e1i c\u00e2y. B\u1ea1n V\u00e2n mua 10 qu\u1ea3 qu\u00fdt, 7 qu\u1ea3 cam\n v\u1edbi gi\u00e1 ti\u1ec1n l\u00e0 17800 \u0111\u1ed3ng. B\u1ea1n Lan mua 12 qu\u1ea3 qu\u00fdt, 6 qu\u1ea3 cam h\u1ebft \n18000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 ti\u1ec1n m\u1ed7i qu\u1ea3 qu\u00fdt v\u00e0 qu\u1ea3 cam h\u1ebft bao nhi\u00eau ?<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

G\u1ecdi x v\u00e0 y l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 ti\u1ec1n m\u1ed7i qu\u1ea3 qu\u00fdt v\u00e0 m\u1ed7i qu\u1ea3 cam. (x > 0; y > 0)<\/p>\n\n\n\n

V\u00e2n mua 10 qu\u1ea3 qu\u00fdt, 7 qu\u1ea3 cam h\u1ebft 17800 \u0111\u1ed3ng n\u00ean ta c\u00f3:<\/p>\n\n\n\n

     10x + 7y = 17800<\/p>\n\n\n\n

Lan mua 12 qu\u1ea3 qu\u00fdt, 6 qu\u1ea3 cam h\u1ebft 18000 \u0111\u1ed3ng n\u00ean ta c\u00f3:<\/p>\n\n\n\n

     12x + 6y = 18000<\/p>\n\n\n\n

T\u1eeb \u0111\u00f3 ta c\u00f3 h\u1ec7:<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

T\u1eeb (2) r\u00fat ra \u0111\u01b0\u1ee3c y = 3000 \u2013 2x, thay v\u00e0o (1) ta \u0111\u01b0\u1ee3c : <\/p>\n\n\n\n

     10x + 7.(3000 \u2013 2x) = 17800 <\/p>\n\n\n\n

\u21d4 10x + 21000 \u2013 14x = 17800 <\/p>\n\n\n\n

\u21d4 4x = 3200 \u21d4 x = 800 (th\u1ecfa m\u00e3n)<\/p>\n\n\n\n

Thay x = 800 v\u00e0o y = 3000 \u2013 2x ta \u0111\u01b0\u1ee3c y = 1400 (th\u1ecfa m\u00e3n)<\/p>\n\n\n\n

V\u1eady gi\u00e1 ti\u1ec1n m\u1ed9t qu\u1ea3 qu\u00fdt l\u00e0 800\u0111 v\u00e0 gi\u00e1 ti\u1ec1n m\u1ed9t qu\u1ea3 cam l\u00e0 1400\u0111. <\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 d\u1ea1ng b\u00e0i gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 h\u1ecdc \u1edf l\u1edbp 8. <\/p>\n\n\n\n

B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <\/p>\n\n\n\n

+ Ch\u1ecdn c\u00e1c \u1ea9n s\u1ed1 v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p cho c\u00e1c \u1ea9n s\u1ed1. <\/p>\n\n\n\n

+ Bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u01b0a bi\u1ebft theo \u1ea9n v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 bi\u1ebft; <\/p>\n\n\n\n

+ L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u01a1ng. <\/p>\n\n\n\n

B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <\/p>\n\n\n\n

B\u01b0\u1edbc 3: Ki\u1ec3m tra xem trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nghi\u1ec7m n\u00e0o th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u1ea9n, nghi\u1ec7m n\u00e0o kh\u00f4ng r\u1ed3i k\u1ebft lu\u1eadn. <\/p>\n\n\n\n

B\u00e0i 4 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> C\u00f3 hai \nd\u00e2y chuy\u1ec1n may \u00e1o s\u01a1 mi. Ng\u00e0y th\u1ee9 nh\u1ea5t c\u1ea3 hai d\u00e2y chuy\u1ec1n may \u0111\u01b0\u1ee3c 930 \n\u00e1o. Ng\u00e0y th\u1ee9 hai day chuy\u1ec1n th\u1ee9 nh\u1ea5t t\u0103ng n\u0103ng su\u1ea5t 18%, d\u00e2y chuy\u1ec1n th\u1ee9 \nhai t\u0103ng n\u0103ng su\u1ea5t 15% n\u00ean c\u1ea3 hai d\u00e2y chuy\u1ec1n n\u00e0y may \u0111\u01b0\u1ee3c 1083 \u00e1o. H\u1ecfi \ntrong ng\u00e0y th\u1ee9 nh\u1ea5t m\u1ed7i d\u00e2y chuy\u1ec1n may \u0111\u01b0\u1ee3c bao nhi\u00eau \u00e1o s\u01a1 mi ?<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

G\u1ecdi s\u1ed1 \u00e1o s\u01a1 mi may \u0111\u01b0\u1ee3c trong ng\u00e0y th\u1ee9 nh\u1ea5t c\u1ee7a d\u00e2y chuy\u1ec1n th\u1ee9 nh\u1ea5t \nv\u00e0 d\u00e2y chuy\u1ec1n th\u1ee9 hai l\u1ea7n l\u01b0\u1ee3t l\u00e0 x v\u00e0 y. (x > 0; y > 0)<\/p>\n\n\n\n

Ng\u00e0y th\u1ee9 nh\u1ea5t c\u1ea3 hai d\u00e2y chuy\u1ec1n may \u0111\u01b0\u1ee3c 930 \u00e1o n\u00ean ta c\u00f3: x + y = 930. <\/p>\n\n\n\n

Ng\u00e0y th\u1ee9 hai: <\/p>\n\n\n\n

d\u00e2y chuy\u1ec1n th\u1ee9 nh\u1ea5t t\u0103ng n\u0103ng su\u1ea5t 18% n\u00ean may \u0111\u01b0\u1ee3c x + 18%.x = 1,18.x \u00e1o<\/p>\n\n\n\n

d\u00e2y chuy\u1ec1n th\u1ee9 hai t\u0103ng n\u0103ng su\u1ea5t 15% n\u00ean may \u0111\u01b0\u1ee3c y + 15%.y = 1,15y \u00e1o <\/ins><\/p>\n\n\n\n

C\u1ea3 hai d\u00e2y chuy\u1ec1n may \u0111\u01b0\u1ee3c 1083 \u00e1o n\u00ean ta c\u00f3: 1,18x + 1,15y = 1083. <\/p>\n\n\n\n

Ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ta \u0111\u01b0\u1ee3c: x = 450, y = 480<\/p>\n\n\n\n

V\u1eady s\u1ed1 \u00e1o s\u01a1 mi d\u00e2y chuy\u1ec1n th\u1ee9 nh\u1ea5t v\u00e0 d\u00e2y chuy\u1ec1n th\u1ee9 hai may \u0111\u01b0\u1ee3c trong ng\u00e0y th\u1ee9 nh\u1ea5t l\u1ea7n l\u01b0\u1ee3t l\u00e0 450 (\u00e1o) v\u00e0 480 (\u00e1o).<\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 d\u1ea1ng b\u00e0i gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 h\u1ecdc \u1edf l\u1edbp 8. <\/p>\n\n\n\n

B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <\/p>\n\n\n\n

+ Ch\u1ecdn c\u00e1c \u1ea9n s\u1ed1 v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p cho c\u00e1c \u1ea9n s\u1ed1. <\/p>\n\n\n\n

+ Bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u01b0a bi\u1ebft theo \u1ea9n v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 bi\u1ebft; <\/p>\n\n\n\n

+ L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u01a1ng. <\/p>\n\n\n\n

B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <\/p>\n\n\n\n

B\u01b0\u1edbc 3: Ki\u1ec3m tra xem trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nghi\u1ec7m n\u00e0o th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u1ea9n, nghi\u1ec7m n\u00e0o kh\u00f4ng r\u1ed3i k\u1ebft lu\u1eadn. <\/p>\n\n\n\n

B\u00e0i 5 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Gi\u1ea3i c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u0110\u01b0a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 h\u1ec7 d\u1ea1ng tam gi\u00e1c b\u1eb1ng c\u00e1ch kh\u1eed d\u1ea7n \u1ea9n s\u1ed1 ta c\u00f3: <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m (x; y; z) = (1; 1; 2). <\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u0110\u01b0a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 h\u1ec7 d\u1ea1ng tam gi\u00e1c b\u1eb1ng c\u00e1ch kh\u1eed d\u1ea7n \u1ea9n s\u1ed1. <\/p>\n\n\n\n

Nh\u00e2n ph\u01b0\u01a1ng tr\u00ecnh (1) v\u1edbi 2 r\u1ed3i c\u1ed9ng v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh (2) v\u00e0 nh\u00e2n ph\u01b0\u01a1ng tr\u00ecnh (1) v\u1edbi (3) r\u1ed3i tr\u1eeb \u0111i ph\u01b0\u01a1ng tr\u00ecnh (3) ta \u0111\u01b0\u1ee3c: <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean ta \u0111\u01b0\u1ee3c \n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m \n<\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

\u0110\u1ec3 gi\u1ea3i h\u1ec7 ba ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n, ta kh\u1eed d\u1ea7n t\u1eebng \u1ea9n s\u1ed1 \u0111\u1ec3 \u0111\u01b0a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng h\u1ec7 tam gi\u00e1c, t\u1eeb \u0111\u00f3 t\u00ecm ra nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. <\/p>\n\n\n\n

B\u00e0i 6 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> M\u1ed9t c\u1eeda \nh\u00e0ng b\u00e1n \u00e1o s\u01a1 mi, qu\u1ea7n nam v\u00e0 v\u00e1y n\u1eef. Ng\u00e0y th\u1ee9 nh\u1ea5t b\u00e1n \u0111\u01b0\u1ee3c 21 \u00e1o, 21 \nqu\u1ea7n v\u00e0 18 v\u00e1y, doanh thu l\u00e0 5.349.000 \u0111\u1ed3ng. Ng\u00e0y th\u1ee9 hai b\u00e1n \u0111\u01b0\u1ee3c 16 \n\u00e1o, 24 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu l\u00e0 5.600.000 \u0111\u1ed3ng. Ng\u00e0y th\u1ee9 ba b\u00e1n \u0111\u01b0\u1ee3c\n 24 \u00e1o, 15 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu l\u00e0 5.259.000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 b\u00e1n m\u1ed7i \n\u00e1o, m\u1ed7i qu\u1ea5n v\u00e0 m\u1ed7i v\u00e1y l\u00e0 bao nhi\u00eau ?<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

G\u1ecdi x, y, z (\u0111\u1ed3ng) l\u1ea7n l\u01b0\u1ee3t l\u00e0 gi\u00e1 ti\u1ec1n m\u1ed7i \u00e1o, qu\u1ea7n v\u00e0 v\u00e1y (0 < x, y, z < 5259000).<\/p>\n\n\n\n

Ng\u00e0y th\u1ee9 nh\u1ea5t b\u00e1n \u0111\u01b0\u1ee3c 21 \u00e1o, 21 qu\u1ea7n v\u00e0 18 v\u00e1y, doanh thu l\u00e0 5.349.000 \u0111\u1ed3ng n\u00ean ta c\u00f3:<\/p>\n\n\n\n

    12x + 21y + 18z = 5.349.000<\/p>\n\n\n\n

Ng\u00e0y th\u1ee9 hai b\u00e1n \u0111\u01b0\u1ee3c 16 \u00e1o, 24 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu l\u00e0 5.600.000 \u0111\u1ed3ng n\u00ean ta c\u00f3:<\/p>\n\n\n\n

    16x + 24y + 12z = 5.600.000<\/p>\n\n\n\n

Ng\u00e0y th\u1ee9 ba b\u00e1n \u0111\u01b0\u1ee3c 24 \u00e1o, 15 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu l\u00e0 5.259.000 \u0111\u1ed3ng n\u00ean ta c\u00f3:<\/p>\n\n\n\n

    24x + 15y + 12z = 5.259.000<\/ins><\/p>\n\n\n\n

T\u1eeb \u0111\u00f3 ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1ea5y (1) \u2013 (2) ta \u0111\u01b0\u1ee3c : y + 3z = 383000.<\/p>\n\n\n\n

Nh\u00e2n 2 v\u00e0o hai v\u1ebf c\u1ee7a (1) r\u1ed3i tr\u1eeb \u0111i (3) ta \u0111\u01b0\u1ee3c: 9y + 8z = 1813000<\/p>\n\n\n\n

Ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

Thay y = 125000, z = 86000 v\u00e0o (1) ta \u0111\u01b0\u1ee3c x = 98000.<\/p>\n\n\n\n

V\u1eady: Gi\u00e1 b\u00e1n m\u1ed7i \u00e1o l\u00e0: 98.000 \u0111\u1ed3ng.<\/p>\n\n\n\n

      Gi\u00e1 b\u00e1n m\u1ed7i qu\u1ea7n l\u00e0: 125.000 \u0111\u1ed3ng.<\/p>\n\n\n\n

      Gi\u00e1 b\u00e1n m\u1ed7i v\u00e1y l\u00e0: 86.000 \u0111\u1ed3ng.<\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 d\u1ea1ng b\u00e0i gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 h\u1ecdc \u1edf l\u1edbp 8. <\/p>\n\n\n\n

B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: <\/p>\n\n\n\n

+ Ch\u1ecdn c\u00e1c \u1ea9n s\u1ed1 v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p cho c\u00e1c \u1ea9n s\u1ed1. <\/p>\n\n\n\n

+ Bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u01b0a bi\u1ebft theo \u1ea9n v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 bi\u1ebft; <\/p>\n\n\n\n

+ L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u01a1ng. <\/p>\n\n\n\n

B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <\/p>\n\n\n\n

B\u01b0\u1edbc 3: Ki\u1ec3m tra xem trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, nghi\u1ec7m n\u00e0o th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u1ea9n, nghi\u1ec7m n\u00e0o kh\u00f4ng r\u1ed3i k\u1ebft lu\u1eadn. <\/p>\n\n\n\n

B\u00e0i 7 (trang 68 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Gi\u1ea3i c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau b\u1eb1ng m\u00e1y t\u00ednh b\u1ecf t\u00fai (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai)<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

H\u01b0\u1edbng d\u1eabn c\u00e1ch gi\u1ea3i c\u00e2u a)<\/em><\/p>\n\n\n\n

N\u1ebfu s\u1eed d\u1ee5ng m\u00e1y t\u00ednh CASIO fx-500 MS ta \u1ea5n li\u00ean ti\u1ebfp d\u00e3y c\u00e1c ph\u00edm<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

th\u1ea5y hi\u1ec7n ra tr\u00ean m\u00e0n h\u00ecnh x = 0,048780487<\/p>\n\n\n\n

\u1ea4n ti\u1ebfp ph\u00edm = ta th\u1ea5y tr\u00ean m\u00e0n h\u00ecnh hi\u1ec7n ra y = -1,170731707<\/p>\n\n\n\n

L\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai ta \u0111\u01b0\u1ee3c nghi\u1ec7m g\u1ea7n \u0111\u00fang c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0<\/p>\n\n\n\n

            (x; y) \u2248 (0,05; -1,17)<\/p>\n\n\n\n

H\u01b0\u1edbng d\u1eabn c\u00e1ch gi\u1ea3i c\u00e2u c)<\/em><\/p>\n\n\n\n

N\u1ebfu s\u1eed d\u1ee5ng m\u00e1y t\u00ednh CASIO fx-500 MS ta \u1ea5n li\u00ean ti\u1ebfp d\u00e3y c\u00e1c ph\u00edm<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

th\u1ea5y hi\u1ec7n ra tr\u00ean m\u00e0n h\u00ecnh x = 0,217821782<\/p>\n\n\n\n

\u1ea4n ti\u1ebfp ph\u00edm = ta th\u1ea5y tr\u00ean m\u00e0n h\u00ecnh hi\u1ec7n ra y = 1,297029703<\/p>\n\n\n\n

\u1ea4n ti\u1ebfp ph\u00edm = ta th\u1ea5y tr\u00ean m\u00e0n h\u00ecnh hi\u1ec7n ra z = -0,386138613<\/p>\n\n\n\n

V\u1eady nghi\u1ec7m g\u1ea7n \u0111\u00fang c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 (l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai)<\/p>\n\n\n\n

            (x; y; z) \u2248 (0,22; 1,30; -0,39)<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

* \u0110\u1ed1i v\u1edbi m\u00e1y t\u00ednh CASIO f(x)\u2013500MS c\u00e1c b\u1ea1n \u1ea5n nh\u01b0 tr\u00ean h\u01b0\u1edbng d\u1eabn. <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u0110\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean, ta \u1ea5n c\u00e1c d\u00e3y ph\u00edm sau : <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

M\u00e0n h\u00ecnh hi\u1ec7n x = 0.1052631579<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u1ea4n ti\u1ebfp \n th\u00ec m\u00e0n h\u00ecnh hi\u1ec7n y = 1.736842105<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u0110\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean ta \u1ea5n c\u00e1c d\u00e3y ph\u00edm sau : <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

M\u00e0n h\u00ecnh hi\u1ec3n th\u1ecb x = \u20134<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u1ea4n ti\u1ebfp \n th\u00ec m\u00e0n h\u00ecnh hi\u1ec3n th\u1ecb y = 1.571428571<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u1ea4n ti\u1ebfp \n th\u00ec m\u00e0n h\u00ecnh hi\u1ec3n th\u1ecb z = 1.714285714<\/p>\n\n\n\n

* \u0110\u1ed1i v\u1edbi c\u00e1c lo\u1ea1i m\u00e1y t\u00ednh CASIO fx\u2013570 v\u00e0 c\u00e1c lo\u1ea1i m\u00e1y VINACAL, \u0111\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00e1c b\u1ea1n \u1ea5n <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

sau \u0111\u00f3 \u1ea5n \nn\u1ebfu nh\u01b0 gi\u1ea3i h\u1ec7 hai ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

\u1ea5n \n n\u1ebfu nh\u01b0 gi\u1ea3i h\u1ec7 ba ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n. <\/p>\n\n\n\n

Sau \u0111\u00f3 nh\u1eadp c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh nh\u01b0 tr\u00ean.<\/p>\n\n\n\n

K\u1ebft qu\u1ea3 s\u1ebd hi\u1ec7n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1, \u0111\u1ec3 k\u1ebft qu\u1ea3 hi\u1ec7n d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n, c\u00e1c b\u1ea1n d\u00f9ng ph\u00edm \n<\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n","protected":false},"excerpt":{"rendered":"

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 63: C\u1eb7p (1; -2) c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 7 kh\u00f4ng ? Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 c\u00f2n c\u00f3 nh\u1eefng nghi\u1ec7m kh\u00e1c n\u1eefa kh\u00f4ng ? L\u1eddi gi\u1ea3i Ta c\u00f3: 3.1-2.(-2) = 7 \u21d2 C\u1eb7p (1; -2) l\u00e0 m\u1ed9t nghi\u1ec7m […]<\/p>\n","protected":false},"author":12,"featured_media":44330,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1633],"tags":[],"yoast_head":"\n[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 3: Ph\u01b0\u01a1ng tr\u00ecnh. H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh\/ B\u00e0i 3: Ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t nhi\u1ec1u \u1ea9n<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/giai-toan-10-chuong-3-phuong-trinh-he-phuong-trinh-bai-3-phuong-trinh-va-he-phuong-trinh-bac-nhat-nhieu-an\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 3: Ph\u01b0\u01a1ng tr\u00ecnh. H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh\/ B\u00e0i 3: Ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t nhi\u1ec1u \u1ea9n\" \/>\n<meta property=\"og:description\" content=\"Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 3 trang 63: C\u1eb7p (1; -2) c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3x \u2013 2y = 7 kh\u00f4ng ? Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 c\u00f2n c\u00f3 nh\u1eefng nghi\u1ec7m kh\u00e1c n\u1eefa kh\u00f4ng ? 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