Question

15£®¡°È«ÃñÔĶÁ¡±ÉîÈëÈËÐÄ£¬ºÃ¶ÁÊ飬¶ÁºÃÊ飬ÈÃÈËÖÕÉíÊÜÒ森ÎÒУÉÏÔ¾ٰìÁË¡°¶ÁÊé½Ú¡±»î¶¯£®ÎªÁ˱íÕÃÓÅÐ㣬Ö÷°ìµ¥Î»ÍõÀÏʦ¸ºÔð¹ºÂò½±Æ·£®Ëû·¢ÏÖ£ºÈôÒÔ2Ö§¸Ö±ÊºÍ3±¾±Ê¼Ç±¾ÎªÒ»·Ý½±Æ·£¬Ôò¿ÉÂò60·Ý½±Æ·£»ÈôÒÔ2Ö§¸Ö±ÊºÍ6±¾±Ê¼Ç±¾ÎªÒ»·Ý½±Æ·£¬Ôò¿ÉÒÔÂò40·Ý½±Æ·£®Éè¸Ö±Êµ¥¼ÛΪxÔª/Ö§£¬±Ê¼Ç±¾µ¥¼ÛΪyÔª/±¾£®
£¨1£©ÇëÓÃxµÄ´úÊýʽ±íʾy£®
£¨2£©ÈôÓÃÕâǮȫ²¿¹ºÂò±Ê¼Ç±¾£¬×ܹ²¿ÉÒÔÂò¼¸±¾£¿
£¨3£©ÈôÍõÀÏʦÓÃÕâǮǡºÃÂò30·ÝͬÑùµÄ½±Æ·£¬¿ÉÒÔÑ¡ÔñaÖ§¸Ö±ÊºÍb±¾±Ê¼Ç±¾×÷Ϊһ·Ý½±Æ·£¨Á½ÖÖ½±Æ·¶¼ÒªÓУ©£¬ÇëÇó³öËùÓпÉÄܵÄa¡¢bÖµ£®

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÁ½ÖÖ¹ºÂò·½°¸×ÜÇ®ÊýÏàͬ£¬¼´¿ÉµÃ³ö¹ØÓÚx¡¢yµÄ¶þÔªÒ»´Î·½³Ì£¬»¯¼òºó¼´¿ÉµÃ³ö½áÂÛ£»
£¨2£©¸ù¾ÝÊýÁ¿=×ÜÇ®Êý¡Âµ¥¼Û½áºÏ£¨1£©½áÂÛ£¬¼´¿ÉÇó³öÄܹ»¹ºÂò±Ê¼Ç±¾µÄ±¾Êý£»
£¨3£©¸ù¾Ý×ÜÇ®ÊýΪ¶¨Öµ½áºÏ£¨1£©½áÂÛ£¬¼´¿ÉµÃ³ö¹ØÓÚa¡¢bµÄ¶þÔªÒ»´Î·½³Ì£¬ÔÙ¸ù¾Ýa¡¢b¾ùΪÕýÕûÊý£¬¼´¿ÉÇó³ö¶þÔªÒ»´Î·½³ÌµÄËùÓÐÕýÕûÊý½â£¬´ËÌâµÃ½â£®

½â´ð ½â£º£¨1£©¸ù¾ÝÌâÒâµÃ£º60£¨2x+3y£©=40£¨2x+6y£©£¬
»¯¼òµÃ£ºy=$\frac{2}{3}$x£®
£¨2£©60£¨2x+3y£©¡Ây=360£®
´ð£ºÈôÓÃÕâǮȫ²¿¹ºÂò±Ê¼Ç±¾£¬×ܹ²¿ÉÒÔÂò360±¾£®
£¨3£©¸ù¾ÝÌâÒâµÃ£º60£¨2x+3y£©=30£¨ax+by£©£¬
¼´4x+6y=ax+by£¬
°Ñy=$\frac{2}{3}$x´úÈëµÃ£º4x+4x=ax+$\frac{2}{3}$bx£¬
ÕûÀíµÃ£ºa+$\frac{2}{3}$b=8£®
¡ßa¡¢b¾ùΪÕýÕûÊý£¬
¡àbΪ3µÄÕûÊý±¶£¬
¡àµ±b=3ʱ£¬a=6£»µ±b=6ʱ£¬a=4£»µ±b=9ʱ£¬a=2£®
¡à$\left\{\begin{array}{l}{a=6}\\{b=3}\end{array}\right.$£¬$\left\{\begin{array}{l}{a=4}\\{b=6}\end{array}\right.$£¬$\left\{\begin{array}{l}{a=2}\\{b=9}\end{array}\right.$£®

µãÆÀ ±¾Ì⿼²éÁ˶þÔªÒ»´Î·½³ÌµÄÓ¦Ó㬽âÌâµÄ¹Ø¼üÊÇ£º£¨1£©¸ù¾ÝÁ½ÖÖ¹ºÂò·½°¸×ÜÇ®ÊýÏàͬ£¬Áгö¹ØÓÚx¡¢yµÄ¶þÔªÒ»´Î·½³Ì£»£¨2£©¸ù¾ÝÊýÁ¿¹Øϵ£¬ÁÐʽ¼ÆË㣻£¨3£©¸ù¾Ý×ÜÇ®ÊýΪ¶¨Öµ½áºÏy=$\frac{2}{3}$x£¬Áгö¹ØÓÚa¡¢bµÄ¶þÔªÒ»´Î·½³Ì£®