《2025年春如金卷课时作业AB本八年级数学上册北师大版》

5. 下列各值中是方程组$\left\{\begin{array}{l} a + b = 3,\\ a - b = 1\end{array}\right.$的解的是(D)
A. $\left\{\begin{array}{l} a = 1,\\ b = 2\end{array}\right.$
B. $\left\{\begin{array}{l} a = 4,\\ b = 5\end{array}\right.$
C. $\left\{\begin{array}{l} a = 3,\\ b = 1\end{array}\right.$
D. $\left\{\begin{array}{l} a = 2,\\ b = 1\end{array}\right.$

答案： D

6. 用加减消元法解二元一次方程组。
(1)$\left\{\begin{array}{l} 3x - y = 9,\\ 2x + y = 11\end{array}\right.$$\left\{\begin{array}{l}x=4, \\ y=3\end{array}\right.$
(2)$\left\{\begin{array}{l} 5x + 2y = 12,\\ 3x + 2y = 6\end{array}\right.$$\left\{\begin{array}{l}x=3, \\ y=-\frac{3}{2}\end{array}\right.$
(3)$\left\{\begin{array}{l} x - 4y = -1,\\ 2x + y = 16\end{array}\right.$$\left\{\begin{array}{l}x=7, \\ y=2\end{array}\right.$
(4)$\left\{\begin{array}{l} 5x + 2y = 25,\\ 3x + 4y = 15\end{array}\right.$$\left\{\begin{array}{l}x=5, \\ y=0\end{array}\right.$
(5)$\left\{\begin{array}{l} 5x + 3y = 6,\\ 2x - 5y = \frac{1}{3}\end{array}\right.$$\left\{\begin{array}{l}x=1, \\ y=\frac{1}{3}\end{array}\right.$
(6)$\left\{\begin{array}{l} 2x + 3y = 6,\\ 3x - 2y = -2\end{array}\right.$$\left\{\begin{array}{l}x=\frac{6}{13}, \\ y=\frac{22}{13}\end{array}\right.$

答案：
(1) $\left\{\begin{array}{l}x=4, \\ y=3\end{array}\right.$
(2) $\left\{\begin{array}{l}x=3, \\ y=-\frac{3}{2}\end{array}\right.$
(3) $\left\{\begin{array}{l}x=7, \\ y=2\end{array}\right.$
(4) $\left\{\begin{array}{l}x=5, \\ y=0\end{array}\right.$
(5) $\left\{\begin{array}{l}x=1, \\ y=\frac{1}{3}\end{array}\right.$
(6) $\left\{\begin{array}{l}x=\frac{6}{13}, \\ y=\frac{22}{13}\end{array}\right.$

7. 若$x$,$y满足\sqrt{2x - 3y + 5} + (2x + 3y - 13)^2 = 0$,则$2x - y$的值为______1。

答案： 1

B)
A. 5
B. 2
C. -3
D. -2

答案： B

9. 解方程：
(1)$\left\{\begin{array}{l} 3x + 4y = 16,\\ 5x - 6y = 33\end{array}\right.$
解：$\left\{\begin{array}{l}x=6, \\ y=-\frac{1}{2}\end{array}\right.$
(2)$\left\{\begin{array}{l} 3(x - 2y) + 8y = 4,\\ \frac{x}{3} + \frac{y}{2} = 2\end{array}\right.$
解：$\left\{\begin{array}{l}x=-\frac{12}{5}, \\ y=\frac{28}{5}\end{array}\right.$

答案：
(1) $\left\{\begin{array}{l}x=6, \\ y=-\frac{1}{2}\end{array}\right.$
(2) $\left\{\begin{array}{l}x=-\frac{12}{5}, \\ y=\frac{28}{5}\end{array}\right.$

10. 已知关于$x$,$y的二元一次方程组\left\{\begin{array}{l} 3x - 5y = 36,\\ bx + ay = -8\end{array}\right.与方程组\left\{\begin{array}{l} 2x + 5y = -26,\\ ax - by = -4\end{array}\right.$有相同的解。
(1)求这两个方程组的相同解；
(2)求$(2a + b)^{2024}$的值。
(1) $\left\{\begin{array}{l}x=2, \\ y=-6\end{array}\right.$
(2) 1

答案：
(1) 由题意, 得 $\left\{\begin{array}{l}2 x+5 y=-26(1), \\ 3 x-5 y=36(2),\end{array}\right.$
(1)+
(2), 得 $5 x=10$,
解得 $x=2$ 。把 $x=2$ 代人
(1), 得 $4+5 y=-26$, 解得
$y=-6$ 。
所以这两个方程组的相同解为 $\left\{\begin{array}{l}x=2, \\ y=-6 。\end{array}\right.$
(2) 把 $\left\{\begin{array}{l}x=2, \\ y=-6\end{array}\right.$ 代人 $\left\{\begin{array}{l}a x-b y=-4, \\ b x+a y=-8,\end{array}\right.$ 得 $\left\{\begin{array}{l}2 a+6 b=-4, \\ 2 b-6 a=-8 。\end{array}\right.$
解此方程组, 得 $a=1, b=-1$,
所以 $(2 a+b)^{2024}=(2-1)^{2024}=1$ 。