10.4 三元一次方程组的解法 (学生版+答案版)2025-2026学年数学人教版七年级下册

　　　　　　　*10.4　三元一次方程组的解法
1.知道解三元一次方程组的基本思想方法是消元，即化“三元”为“二元”．2．*能解简单的三元一次方程组(选学).
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　三元一次方程组
1．方程组含有 个未知数，且含有未知数的式子都是整式，含有未知数的项的次数都是 ，一共有三个方程，像这样的方程组叫作三元一次方程组．
练习1　下列是三元一次方程组的是( ).
A． B．
C． D．
知识点二　三元一次方程组的解法
2．解三元一次方程组的具体步骤．
(1)变形：通过加减消元或代入消元把三元一次方程组化成 方程组．
(2)求解：求解二元一次方程组．
(3)回代：将求得的二元一次方程组的解代入原方程组中一个适当的方程中，得到一个一元一次方程．
(4)求解：解一元一次方程得到第三个未知数的值．
(5)写解：用“{”写出方程组的解．
练习2　(教材P108例1变式)解三元一次方程组
1．下列方程组中，是三元一次方程组的是( ).
A． B．
C． D．
2．解方程组如果要使运算简便，那么消元时最好应( ).
A．先消去x B．先消去y
C．先消去z D．先消去常数项
3．解方程组以下解法不正确的是( ).
A．由①，②消去z，再由①，③消去z
B．由①，③消去z，再由②，③消去z
C．由①，②消去z，再由①，③消去y
D．由①，③消去y，再由①，②消去y
4．有甲、乙、丙三种商品，若购甲1件、乙2件、丙3件，共需136元；若购甲3件、乙2件、丙1件，共需240元，则购甲、乙、丙三种商品各1件共需 ( ).
A．94元 B．92元
C．91元 D．90元
5．已知＝＝，且3a＋2b－c＝12，则a＋b＋c的值等于________．
6．设“，，”分别表示三种不同的物体，如图，前面两架天平保持平衡，如果要使第三架也平衡，那么“？”处可以放的物体为( ).
A． B．
C． D．
7．【数学问题】解方程组
【思路分析】七年级(5)班数学探究小组，观察后发现方程①的左边是x＋y，而方程②的括号里也是x＋y，他想到可以把x＋y视为一个整体，把方程①直接代入到方程②中，这样，就可以将方程②直接转化为一元一次方程，从而达到“消元”的目的．
(1)【完成解答】请你按照探究小组的思路，完成解方程组的过程．
(2)你还能用其他的方法来求得方程组的解吗？
(3)【迁移运用】请你按照探究小组的方法，解方程组
8．一方有难八方支援，某市政府筹集了抗洪必需物资138 t打算运往灾区．现有甲、乙、丙三种车型供选择，每辆车的运载能力(假设每辆车均满载)和运费如下表所示：
车型 甲 乙 丙
汽车运载量/(t/辆) 6 9 10
汽车运费/(元/辆) 500 600 600
(1)若全部物资都用甲、乙两种车型来运送，需运费10 000元，分别需要甲、乙两种车型各几辆？
(2)为了节约运费，该市政府可以调用甲、乙、丙三种车型参与运送，已知它们的总辆数为16，要求三种车型同时参与运货，请用列方程组的方法求出满足条件的所有运送方案．
(3)在(2)的基础上，哪种方案的运费最少？最少的运费是多少元？INCLUDEPICTURE "节2.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\节2.TIF" \* MERGEFORMATINET
　　　　　　　*10.4　三元一次方程组的解法
INCLUDEPICTURE "学习目标上.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET
1.知道解三元一次方程组的基本思想方法是消元，即化“三元”为“二元”．2．*能解简单的三元一次方程组(选学).
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
知识点一　三元一次方程组
1．方程组含有三个未知数，且含有未知数的式子都是整式，含有未知数的项的次数都是1，一共有三个方程，像这样的方程组叫作三元一次方程组．
练习1　下列是三元一次方程组的是(　B　).
A． B．
C． D．
知识点二　三元一次方程组的解法
2．解三元一次方程组的具体步骤．
(1)变形：通过加减消元或代入消元把三元一次方程组化成二元一次方程组．
(2)求解：求解二元一次方程组．
(3)回代：将求得的二元一次方程组的解代入原方程组中一个适当的方程中，得到一个一元一次方程．
(4)求解：解一元一次方程得到第三个未知数的值．
(5)写解：用“{”写出方程组的解．
练习2　(教材P108例1变式)解三元一次方程组
【答案】
知识点三　构造三元一次方程组求值
练习3　(教材P109例2变式)在等式y＝ax2＋bx＋c中，当x＝－2时，y＝9；当x＝0时，y＝3；当x＝2时，y＝5.求a，b，c的值．
【答案】a＝1，b＝－1，c＝3.
eq \o(\s\up7( INCLUDEPICTURE "课后练习.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 基础巩固
1．下列方程组中，是三元一次方程组的是(　D　).
A． B．
C． D．
2．解方程组如果要使运算简便，那么消元时最好应(　B　).
A．先消去x B．先消去y
C．先消去z D．先消去常数项
3．解方程组以下解法不正确的是(　C　).
A．由①，②消去z，再由①，③消去z
B．由①，③消去z，再由②，③消去z
C．由①，②消去z，再由①，③消去y
D．由①，③消去y，再由①，②消去y
4．有甲、乙、丙三种商品，若购甲1件、乙2件、丙3件，共需136元；若购甲3件、乙2件、丙1件，共需240元，则购甲、乙、丙三种商品各1件共需 (　A　).
A．94元 B．92元
C．91元 D．90元
5．已知＝＝，且3a＋2b－c＝12，则a＋b＋c的值等于________．
【答案】15
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 能力达标
6．设“ INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET ， INCLUDEPICTURE "L26CGD7SX60A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60A.TIF" \* MERGEFORMATINET ， INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET ”分别表示三种不同的物体，如图，前面两架天平保持平衡，如果要使第三架也平衡，那么“？”处可以放的物体为(　C　).
INCLUDEPICTURE "L26CGD7SX60.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60.TIF" \* MERGEFORMATINET
A． INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60+.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "L26CGD7SX60-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX60-.TIF" \* MERGEFORMATINET
7．【数学问题】解方程组
【思路分析】七年级(5)班数学探究小组，观察后发现方程①的左边是x＋y，而方程②的括号里也是x＋y，他想到可以把x＋y视为一个整体，把方程①直接代入到方程②中，这样，就可以将方程②直接转化为一元一次方程，从而达到“消元”的目的．
(1)【完成解答】请你按照探究小组的思路，完成解方程组的过程．
(2)你还能用其他的方法来求得方程组的解吗？
(3)【迁移运用】请你按照探究小组的方法，解方程组
【解】(1)把①代入②，得5x－2×2＝6，
解得x＝2.
把x＝2代入①，得2＋y＝2，
解得y＝0，
所以方程组的解为
(2)由①，得x＝2－y，③
把③代入②，得5(2－y)－2[(2－y)＋y]＝6，解得y＝0，
把y＝0代入③，得x＝2，
所以方程组的解为(答案不唯一)
(3)把①代入③，得3＋c＝0，解得c＝－3.把c＝－3代入②，得5a－9＝1，解得a＝2.把a＝2代入①，得2＋b＝3，解得b＝1.
所以方程组的解为
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 挑战创新
8．一方有难八方支援，某市政府筹集了抗洪必需物资138 t打算运往灾区．现有甲、乙、丙三种车型供选择，每辆车的运载能力(假设每辆车均满载)和运费如下表所示：
车型 甲 乙 丙
汽车运载量/(t/辆) 6 9 10
汽车运费/(元/辆) 500 600 600
(1)若全部物资都用甲、乙两种车型来运送，需运费10 000元，分别需要甲、乙两种车型各几辆？
(2)为了节约运费，该市政府可以调用甲、乙、丙三种车型参与运送，已知它们的总辆数为16，要求三种车型同时参与运货，请用列方程组的方法求出满足条件的所有运送方案．
(3)在(2)的基础上，哪种方案的运费最少？最少的运费是多少元？
【解】(1)设需要甲种车型a辆，乙种车型b辆．
根据题意，得
解得
答：需要甲种车型8辆，乙种车型10辆．
(2)设三种车型同时参与时，需要甲种车型x辆，乙种车型y辆，丙种车型z辆．
根据题意，得
①×10－②，
得4x＋y＝22，即y＝22－4x.
因为x，y，z均是非负整数，且三种车型共16辆，要求同时参与运货，
所以x≤5，y≤14，且z≥1，
所以x的取值可以为3，4，5.
解得或或
答：共有三种运送方案：①甲种车型3辆，乙种车型10辆，丙种车型3辆；②甲种车型4辆，乙种车型6辆，丙种车型6辆；③甲种车型5辆，乙种车型2辆，丙种车型9辆．
(3)三种方案的运费分别是①3×500＋10×600＋3×600＝9 300(元)；
②4×500＋6×600＋6×600＝9 200(元)；
③5×500＋2×600＋9×600＝9 100(元).
9 100<9 200<9 300，
答：甲种车型5辆、乙种车型2辆、丙种车型9辆时运费最少，最少的运费是9 100元．