二元一次方程组解应用题
\u89e3\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u5e94\u7528\u9898\u89e3\uff1a\uff081\uff09\u8bbe\u4ed6\u5bb6\u8fd9\u6708\u4f7f\u7528\u5cf0\u3001\u8c37\u7535\u5206\u522b\u4e3ax\uff0cy\u5343\u74e6\u65f6\uff0c\u90a3\u4e48\uff0c\u53ef\u5217\u65b9\u7a0b\u7ec4\uff1a
0.56x+0.28y=95.2;0.53(x+y)=95.2+10.8
\u89e3\u65b9\u7a0b\u7ec4\u53ef\u5f97\uff1ax=140,y=60
(2)\u8bbe\u7528\u5cf0\u3001\u8c37\u7535\u5206\u522bx,y\u5343\u74e6\u65f6\uff0c\u8981\u4f7f\u201c\u5cf0\u8c37\u7535\u201d\u5408\u7b97\uff0c\u5219\u4e00\u5e94\u8be5\u6709\uff1a
0.56x+0.28y<0.53(x+y),\u53733x<25y
\u6b64\u65f6\uff0c\u5cf0\u7535\u4e0d\u8d85\u8fc7\u603b\u7535\u91cf\u768425/(3+25)\u7ea689.3%
1\u3001\u89e3\uff1a
\u8bbe\u53ef\u83b7\u5f97\u5229\u6da6\u4e3aw\u5143\uff0c\u9500\u552e\u5355\u4ef7\u4e3ax\u5143
\u6839\u636e\u9898\u610f\u53ef\u5f97\uff0c
w=[200(13.5-x)+500]*x-2.5*[200(13.5-x)+500]
=-200x2+3700x-8000
=-200(x-9.25)2+9112.5
\u6240\u4ee5\uff0c\u5f53\u9500\u552e\u5355\u4ef7\u5b9a\u4e3a9.25\u5143\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a9112.5\u5143
\u7b54\uff1a\u9500\u552e\u5355\u4ef7\u5b9a\u4e3a9.25\u5143\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a9112.5\u5143
2\u3001\u89e3\uff1a
\u8bbe\u53ef\u83b7\u5f97\u5229\u6da6\u4e3aw\u5143\uff0c\u9500\u552e\u5355\u4ef7\u4e3ax\u5143
\u6839\u636e\u9898\u610f\u53ef\u5f97\uff0c
w=[400-20\uff08x-30\uff09]*x-20*[400-20(x-30)]
=-20x2+1400x-2000
=-20(x-35)2+22500
\u6240\u4ee5\uff0c\u5f53\u9500\u552e\u5355\u4ef7\u5b9a\u4e3a35\u5143\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a22500\u5143
\u7b54\uff1a\u9500\u552e\u5355\u4ef7\u5b9a\u4e3a35\u5143\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a22500\u5143\u3002
3\u3001\u89e3\uff1a
\u8bbe\u53ef\u83b7\u5f97\u5229\u6da6\u4e3aw\u5143\uff0c\u65c5\u884c\u56e2\u7684\u4eba\u6570\u4e3ax\u4eba
\u6839\u636e\u9898\u610f\u53ef\u5f97\uff0c
w=[800-10\uff08x-30)]*x
=-10x2+1100x
=-10(x-55)+30250
\u6240\u4ee5\uff0c\u5f53\u65c5\u884c\u56e2\u7684\u4eba\u6570\u4e3a55\u4eba\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a30250\u5143
\u7b54\uff1a\u65c5\u884c\u56e2\u7684\u4eba\u6570\u4e3a55\u4eba\u65f6\uff0c\u53ef\u83b7\u5f97\u6700\u5927\u5229\u6da6\uff0c\u4e3a30250\u5143\u3002
依题意列方程组：
4*4+3*(x-4)=y-16 (1)
1*2+6*(x-1)=y (2)
由(1)得：16+3x-12=y-16
3x+4=y-16
3x-y+20=0 (3)
由(2)得：2+6x-6=y
6x-y-4=0 (4)
(4)-(3)：3x-24=0
x=8 (人) (5)
(5)代入(4)：6*8-y-4=0
44-y=0
y=44(枝)
x=8 (人) 、y=44(枝)
答：同学有8人，铅笔有44枝。
绛旓細瑙ｏ細璁炬煇骞村伐涓氬簾姘存湁x鍚紝鍒欏煄闀囩敓娲绘薄姘存湁y鍚ㄣ92%x+57%y=572*72% 锛1锛墄+y=572 锛2锛夌敱锛2锛夊緱锛歽=572-x 锛3锛夊皢锛4锛変唬鍏ワ紙2锛夌殑x鈮245 灏唜鈮245浠ｅ叆1寰 y=327 鎵浠 x=245 y=327 绛旓細鏌愬勾宸ヤ笟搴熸按鐨勬帓鏀鹃噺涓245鍚紝鍩庨晣鐢熸椿姹℃按鐨勬帓鏀鹃噺涓327鍚ㄣ備笉浼氬啀闂垜...
绛旓細鎴戣嚜宸辩紪鐨搴旂敤棰锛氾紙1锛変竴涓瀛愰噷鏈夐浮鍜屽厰瀛愶紝鍏朵腑涓鍏辨湁澶20涓紝鑴50鍙紝璇烽棶楦℃湁澶氬皯涓紝鍏斿瓙鏈夊灏戜釜锛熻В锛氳楦℃湁x涓紝鍏斿瓙鏈墆涓.x+y=20 2x+4y=50 瑙ｅ緱锛歺=15 ,y=5 楦℃湁15涓紝鍏斿瓙鏈5涓.(2)灏忔槑涔版按鏋滐紝鑻规灉姣忓崈鍏14鍏冿紝棣欒晧姣忓崈鍏10鍏冿紝涓鍏辫姳浜170鍏冿紝涓ょ姘存灉涓鍏15鍗冨厠...
绛旓細浜屽厓涓娆℃柟绋嬬粍搴旂敤棰 1. 涓娆＄銆佹帓鐞冩瘮璧,鍏辨湁48涓槦,520鍚嶈繍鍔ㄥ憳鍙傚姞,鍏朵腑绡悆闃熸瘡闃10鍚,鎺掔悆闃熸瘡闃12鍚,姹傜銆佹帓鐞冨悇鏈夊灏戦槦鍙傝禌? 2. 鏌愬巶涔拌繘鐢层佷箼涓ょ鏉愭枡鍏56鍚,鐢ㄥ幓9860鍏冦傝嫢鐢茬鏉愭枡姣忓惃190鍏,涔欑鏉愭枡姣忓惃160鍏,鍒欎袱绉嶆潗鏂欏悇涔板灏戝惃? 3. 鏌愪汉鐢24000鍏冧拱杩涚敳銆佷箼涓ょ鑲＄エ,鍦ㄧ敳鑲＄エ鍗...
绛旓細鐢浜屽厓涓娆℃柟绋鏉ヨВ鍐宠闂 宸茬煡璇ユ梾娓稿洟鍙綇鏅氶棿锛屾墍浠ヨ豹鍗庨棿灏变笉鐢ㄨ冭檻浜嗐傝鏃呮父鍥㈠叡浣忎簡涓変汉闂翠负X锛涗簩浜洪棿涓篩 宸茬煡鏃呮父鍥㈡湁50浜 鍒楀紡 3x + 2y =50 锛堝紡 1锛夐厭搴楁墦浜旀姌锛屽氨鏄环鏍奸兘闄嶄簡涓鍗娿備竴澶╃殑鑺辫垂涓1510 鍒楀紡 50%锛150x+140y锛=1510 鍖栬В 150x+140y =3020 15x+14y = 30...
绛旓細瑙ｏ細璁捐矾涓簒鍗冪背锛 涓婂潯璺负y鍗冪背锛屼笅鍧¤矾鍒欎负142-x-y銆傛嵁棰樻剰锛屽緱鏂圭▼缁 x/30+y/28+(142-x-y)/35=4.5 x/30+y/35+(142-x-y)/28=4.7 2x+3y=186 鈶 x+3y=156 鈶 鈶-鈶″緱 x=30 鎶妜=30浠ｄ汉鈶 30+3y=156 3y=126 y=42 142-x-y=70 绛旓細杩欐骞宠矾鏈30鍗冪背锛屽幓...
绛旓細1銆佽В锛氳A鐐硅窛鍖楀北绔欑殑璺濈涓篨 锛屾苯杞︿粠A鐐硅繑鍥炵殑璺濈涓篩 2X+Y=18 锛2Y+X锛/60=X/4 瑙ｅ緱 X=2 Y=14 绛旓細A鐐硅窛鍖楀北绔欑殑璺濈涓2鍗冪背銆2銆佽В锛氳鍘熷叚浣嶆暟鐨勫悗浜斾綅鏁颁负X 鏂板叚浣嶆暟鏄痀 10X+1=Y Y=3*锛100000+X锛夎В寰 X=42857 Y=428571 鍘熷叚浣嶆暟鏄142857 绛旓細 鍘熷叚浣嶆暟鏄142857...
绛旓細瑙ｈ锛氱敳閫熷害涓簒鍗冪背/鏃,涔欓熷害涓簓鍗冪背/鏃 鍒欙細x/y=2/3 1.5y-(1.5+15/60)x=24 瑙ｅ緱:x=48 y=72 涓鸿繋鎺モ滃缓鍥60鍛ㄥ勾鈥濆浗搴嗭紝鎴戝競鍑嗗鐢ㄧ伅楗扮編鍖栫孩鏃楄矾锛岄渶閲囩敤A銆丅涓ょ涓嶅悓绫诲瀷鐨勭伅绗200涓紝涓擝鐏鐨勪釜鏁版槸A鐏鐨2/3.锛堢敤涓鍏冧竴娆℃柟绋锛夛紙1锛夋眰A銆丅涓ょ鐏鍚勯渶澶氬皯涓紵瑙...
绛旓細瑙ｏ細54鍒嗛挓=0.9灏忔椂锛42鍒嗛挓=0.7灏忔椂 璁句笂鍧¤矾a鍗冪背锛屽钩璺痓鍗冪背锛屾牴鎹鎰 a/3+b/4=0.9(1)a/5+b/4=0.6(2)涓ゅ紡鐩稿噺 a(1/3-1/5)=0.3 a=2.25 浠ｅ叆锛1锛塨=0.6 鎵浠ョ敳鍒颁箼璺▼=2.25+0.6=2.85鍗冪背 3銆佺敤鍚嵂30%鍜75%鐨勪袱绉嶉槻鑵愯嵂姘达紝閰嶅埗鍚嵂50%鐨勯槻鑵愯嵂姘18KG锛...
绛旓細1.璁鹃摱鐗屾湁x鏋氾紝閾滅墝鏈墆鏋氾紝鍒欓噾鐗屾湁x+y+2鏋 鍒鏂圭▼缁2x+2y+2=100 x+7=y 瑙ｅ緱x=21锛寉=28 绛旓細閾剁墝鏈21鏋氾紝閾滅墝鏈28鏋氾紝鍒欓噾鐗屾湁51鏋 2.璁炬湁瀛︾敓x鍚嶏紝杞杈 鍒楁柟绋嬬粍x=45y+15 x=60锛坹-1锛夎В寰梮=240锛寉=5 绛旓細鏈240鍚嶅鐢燂紝5杈嗚溅 3.璁惧強鏍肩殑鏈墄浜猴紝涓嶅強鏍肩殑鏈墆浜 鍒...
绛旓細璁惧簲鍒嗛厤x浜虹敓浜ц灪鏍,y浜虹敓浜ц灪姣嶏紝鏍规嵁棰樻剰鍒鏂圭▼锛歺+y=60 14*2x=20y 瑙ｅ緱锛歺=25 y=60-x=35 绛旓細搴斿垎閰25浜虹敓浜ц灪鏍擄紝35浜虹敓浜ц灪姣嶏紝鑳戒娇鐢熶骇鍑虹殑铻烘爴鍜岃灪姣嶅垰濂介厤濂椼
