Question

12£®ÒÑÖª$\left\{\begin{array}{l}{x=3}\\{y=4}\end{array}\right.$£¬$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$¶¼ÊÇ·½³Ìax+by=22µÄ½â£¬ÊÔÅжϣº$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$ÊDz»ÊÇÕâ¸ö·½³ÌµÄ½â£®

Answer 1

·ÖÎö ¸ù¾ÝÒÑÖªÌõ¼þ¿ÉÒÔÁгö¹ØÓÚa¡¢bµÄ·½³Ì×é$\left\{\begin{array}{l}{3a+4b=22}\\{a+5b=22}\end{array}\right.$£¬Í¨¹ý½â¸Ã·½³Ì×éµÃµ½a¡¢bµÄÖµ£»È»ºó½«$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$´úÈë½øÐÐÑéÖ¤¼´¿É£®

½â´ð ½â£º¡ß$\left\{\begin{array}{l}{x=3}\\{y=4}\end{array}\right.$£¬$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$¶¼ÊÇ·½³Ìax+by=22µÄ½â£¬
¡à$\left\{\begin{array}{l}{3a+4b=22}\\{a+5b=22}\end{array}\right.$£¬
½âµÃ$\left\{\begin{array}{l}{a=2}\\{b=4}\end{array}\right.$£®
¡à¸Ã·½³ÌÊÇ2x+4y=22£¬¼´x+2y=11£®
°Ñ$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$´úÈ룬µÃ
×ó±ß=5+2¡Á4=13¡ÙÓұߣ¬
¡à$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$²»ÊÇÕâ¸ö·½³ÌµÄ½â£®

µãÆÀ ±¾Ì⿼²éÁ˶þÔªÒ»´Î·½³ÌµÄ½â£®Í¨¹ý½âϵÊý·½³ÌÇóµÃa¡¢bµÄÖµÊǽâÌâµÄ¹Ø¼ü£®