《2025年春如金卷课时作业AB本八年级数学上册北师大版》

解方程组：
(1)$\left\{\begin{array}{l} 3x+y=10,\\ 2x-y=5;\end{array}\right. $ (2)$\left\{\begin{array}{l} y=x-2,\\ x+y=6;\end{array}\right. $
(3)$\left\{\begin{array}{l} 3x+4y=6,\\ 5x+2y=10;\end{array}\right. $ (4)$\left\{\begin{array}{l} 4x-3y=5,\\ 2x+y=5;\end{array}\right. $
(5)$\left\{\begin{array}{l} \frac {4x}{3}+\frac {3}{2}y=\frac {1}{6},\\ 7x-3y=\frac {9}{2};\end{array}\right. $ (6)$\left\{\begin{array}{l} y=3x-1,\\ 2x+4y=24;\end{array}\right. $
(7)$\left\{\begin{array}{l} 3x-2y=2,\\ 5x+4y=1;\end{array}\right. $ (8)$\left\{\begin{array}{l} \frac {x+y}{2}+\frac {x-y}{3}=6,\\ 4(x-y)=3(x+y)。\end{array}\right. $

答案：
(1)$\left\{\begin{array}{l} 3x+y=10\enclose{circle} {1}\\ 2x-y=5\enclose{circle} {2}\end{array}\right. ,$
$\enclose{circle} {1}+\enclose{circle} {2}$得$3x+2x+y-y=10+5,$
$5x=15,$
解得:$x=3,$
将$x=3$代入②得$6-y=5,$
解得:$y=1,$
∴方程组的解为$\left\{\begin{array}{l} x=3\\ y=1\end{array}\right. $。
(2)$\left\{\begin{array}{l} y=x-2\enclose{circle} {1}\\ x+y=6\enclose{circle} {2}\end{array}\right. ,$
把①代入②,得$x+x-2=6,$
解得$x=4,$
把$x=4$代入①,得$y=4-2=2,$
∴方程组的解为$\left\{\begin{array}{l} x=4\\ y=2\end{array}\right. ;$
(3)$\left\{\begin{array}{l} 3x+4y=6\enclose{circle} {1}\\ 5x+2y=10\enclose{circle} {2}\end{array}\right. ,$
$\enclose{circle} {2}×2$,得$10x+4y=20\enclose{circle} {3},$
$\enclose{circle} {3}-\enclose{circle} {1}$,得$7x=14,$
解得:$x=2,$
把$x=2$代入①,得$3×2+4y=6,$
解得:$y=0,$
∴方程组的解为$\left\{\begin{array}{l} x=2\\ y=0\end{array}\right. $。
(4)$\left\{\begin{array}{l} 4x-3y=5\enclose{circle} {1}\\ 2x+y=5\enclose{circle} {2}\end{array}\right. ,$
$\enclose{circle} {2}×2-\enclose{circle} {1}$,得:$5y=5,$
解得:$y=1,$
把$y=1$代入①,得:$4x-3=5,$
解得:$x=2,$
∴方程组的解为$\left\{\begin{array}{l} x=2\\ y=1\end{array}\right. ;$
(5)方程组整理得$\left\{\begin{array}{l} 8x+9y=1\enclose{circle} {1}\\ 7x-3y=\frac {9}{2}\enclose{circle} {2}\end{array}\right. ,$
$\enclose{circle} {2}×3+\enclose{circle} {1}$,得:$29x=\frac {29}{2},$
解得$x=\frac {1}{2},$
把$x=\frac {1}{2}$代入①,得:$4+9y=1,$
解得:$y=-\frac {1}{3},$
∴方程组的解为$\left\{\begin{array}{l} x=\frac {1}{2}\\ y=-\frac {1}{3}\end{array}\right. $。
(6)将原方程组标号得$\left\{\begin{array}{l} y=3x-1\enclose{circle} {1}\\ 2x+4y=24\enclose{circle} {2}\end{array}\right. ,$
将①代入②得$2x+4(3x-1)=24,$
$\therefore x=2,$
将$x=2$代入①得$y=5,$
$\therefore \left\{\begin{array}{l} x=2\\ y=5\end{array}\right. ;$
(7)将原方程组标号得$\left\{\begin{array}{l} 3x-2y=2\enclose{circle} {1}\\ 5x+4y=1\enclose{circle} {2}\end{array}\right. ,$
$\enclose{circle} {1}×2$得:$6x-4y=4\enclose{circle} {3},$
$\enclose{circle} {2}+\enclose{circle} {3}$得:$11x=5,$
$\therefore x=\frac {5}{11},$
将$x=\frac {5}{11}$代入①得:
$\frac {15}{11}-2y=2,$
$\therefore y=-\frac {7}{22},$
$\therefore \left\{\begin{array}{l} x=\frac {5}{11}\\ y=-\frac {7}{22}\end{array}\right. ;$
(8)将原方程组标号得$\left\{\begin{array}{l} \frac {x+y}{2}+\frac {x-y}{3}=6\enclose{circle} {1}\\ 4(x-y)=3(x+y)\enclose{circle} {2}\end{array}\right. ,$
整理①得$3(x+y)+2(x-y)=36\enclose{circle} {3},$
将②代入③得$4(x-y)+2(x-y)=36,$
解得$x-y=6\enclose{circle} {4},$
将④代入③得$3(x+y)+12=36,$
解得$x+y=8\enclose{circle} {5},$
$\enclose{circle} {4}+\enclose{circle} {5}$得$2x=14,$
$\therefore x=7,$
将$x=7$代入⑤,得$y=1,$
$\therefore \left\{\begin{array}{l} x=7\\ y=1\end{array}\right. $。