《2025年课堂点睛七年级数学上册沪科版》

1. 用加减消元法解方程组$\left\{\begin{array}{l} 2x+y= 3,①\\ x-y= 4,②\end{array} \right. $适合的方法是(B)
A.① - ②
B.② + ①
C.①×2 + ②
D.②×2 + ①

答案： B

2. 解方程组$\left\{\begin{array}{l} 2x-3y= -1,①\\ 2x+3y= 5,②\end{array} \right. $既可以用①+②消去未知数y,也可以用②-①或①-②消去未知数x.

答案： ①+② ②-①或①-②

3. (教材第114页练习第1题变式)用加减法解下列方程：
(1)(2024年广西自治区)$\left\{\begin{array}{l} x+2y= 3,①\\ x-2y= 1;②\end{array} \right. $
(2)$\left\{\begin{array}{l} 3x-y= -4,①\\ x-2y= -3.②\end{array} \right. $

答案：
(1)解:①+②,得2x=4,解得x=2. ①-②,得4y=2,解得$ y=\frac{1}{2} $.所以$ \left\{\begin{array}{l} x=2,\\ y=\frac{1}{2}.\end{array}\right. $
(2)解:①×2,得6x-2y=-8,③. ③-②,得5x=-5,解得x=-1. 把x=-1代入①中,得-3-y=-4,解得y=1.所以$ \left\{\begin{array}{l} x=-1,\\ y=1.\end{array}\right. $

4. (寿春中学单元卷)解方程组：①$\left\{\begin{array}{l} y= 2x-1,\\ 7x+5y= 8;\end{array} \right. $②$\left\{\begin{array}{l} 8x+6y= 25,\\ 17x-6y= 48,\end{array} \right. $在下列提供的两题的解法中,较为简便的是(C)
A.①②均用代入法
B.①②均用加减法
C.①用代入法,②用加减法
D.①用加减法,②用代入法

答案： C

5. (教材第115页练习第1题变式)解下列方程组：
(1)$\left\{\begin{array}{l} 3(x-1)= y+5,①\\ \frac {y-1}{3}= \frac {x}{5}+1;②\end{array} \right. $
(2)$\left\{\begin{array}{l} 2(x-150)= 5(3y+50),\\ 10\% x+60\% y= \frac {8.5}{100}×800.\end{array} \right. $

答案：
(1)解:将原方程组化简,得$ \left\{\begin{array}{l} 3x-y=8,\enclose{circle}{3}\\ 5y-3x=20.\enclose{circle}{4}\end{array}\right. $ ③+④得4y=28,解得y=7,把y=7代入③,得3x-7=8,解得x=5,所以$ \left\{\begin{array}{l} x=5,\\ y=7.\end{array}\right. $
(2)解:把原方程组化简,得$ \left\{\begin{array}{l} 2x-15y=550,\enclose{circle}{1}\\ x+6y=680.\enclose{circle}{2}\end{array}\right. $ ②×2,得2x+12y=1360. ③,③-①,得27y=810,y=30. 把y=30代入②,得x+180=680,x=500. 所以$ \left\{\begin{array}{l} x=500,\\ y=30.\end{array}\right. $

6. 已知x,y满足方程组$\left\{\begin{array}{l} 4x+3y= -1,\\ 2x+y= 3,\end{array} \right. 则x+y$的值为-2.

答案： -2

【变式】解方程组：$\left\{\begin{array}{l} 4x+3y= 3,①\\ 3x-2y= 15.②\end{array} \right. $

答案： 解:①×2,得8x+6y=6,③,②×3,得9x-6y=45,④,③+④,得17x=51,解得x=3. 把x=3代入①中,得4×3+3y=3,解得y=-3. 所以$ \left\{\begin{array}{l} x=3,\\ y=-3.\end{array}\right. $