《2025年优秀生快乐假期每一天全新暑假作业本七年级合订本延边人民出版社》

1. 满足方程$x - 2y = 4$的$x$、$y$的一组解是(C)
A. $\left\{\begin{array}{l} x = 0,\\ y = 2\end{array}\right. $
B. $\left\{\begin{array}{l} x = 4,\\ y = 1\end{array}\right. $
C. $\left\{\begin{array}{l} x = 0,\\ y = -2\end{array}\right. $
D. $\left\{\begin{array}{l} x = 4,\\ y = -1\end{array}\right. $

答案： C

2. 方程组$\left\{\begin{array}{l} 3x - 5y = 6,\\ x + 4y = -15\end{array}\right. $的解是(C)
A. $\left\{\begin{array}{l} x = -3,\\ y = 3\end{array}\right. $
B. $\left\{\begin{array}{l} x = 7,\\ y = 3\end{array}\right. $
C. $\left\{\begin{array}{l} x = -3,\\ y = -3\end{array}\right. $
D. $\left\{\begin{array}{l} x = 3,\\ y = -3\end{array}\right. $

答案： C

3. 已知方程组$\left\{\begin{array}{l} 4x + 3y = 1,\\ kx - (k - 1)y = 3\end{array}\right. $的解满足$x + y = 0$，则$k$的值等于(A)
A. $2$
B. $10$
C. $11$
D. $12$

答案： A

4. 若$ax + 6(a - 1)y = 3$是关于$x$、$y$的二元一次方程，则$a$的取值范围为(C)
A. $a \neq 0$
B. $a \neq 1$
C. $a \neq 0$且$a \neq 1$
D. $a \neq 0$或$a \neq 1$

答案： C

5. 买苹果和梨共$100$千克，其中苹果的质量比梨的质量的$2$倍少$8$千克，求苹果和梨各买了多少. 若设买苹果$x$千克，买梨$y$千克，则列出的方程组应是(D)
A. $\left\{\begin{array}{l} x + y = 100,\\ y = 2x + 8\end{array}\right. $
B. $\left\{\begin{array}{l} x + y = 100,\\ y = 2x - 8\end{array}\right. $
C. $\left\{\begin{array}{l} x + y = 100,\\ x = 2y + 8\end{array}\right. $
D. $\left\{\begin{array}{l} x + y = 100,\\ x = 2y - 8\end{array}\right. $

答案： D

1. 已知$x = 1 - t$，$y = 2 - 3t$，用含$x$的代数式表示$y$的结果是$y=3x-1$.

答案： $y=3x-1$

2. 已知$x + 4y - 3z = 0$，$4x - 5y + 2z = 0$，则$x : y : z = $$1:2:3$.

答案： $1:2:3$

3. 已知$\left\{\begin{array}{l} x = 1,\\ y = -2\end{array}\right. $和$\left\{\begin{array}{l} x = 2,\\ y = 0\end{array}\right. $都是方程$ax - by = 1$的解，则$a = $$\frac {1}{2}$，$b = $$\frac {1}{4}$.

答案： $\frac {1}{2},\frac {1}{4}$

4. 已知$5a^{y + 5}b^{3x}$与$-4a^{2x}b^{2 - 4y}$是同类项，则$x = $2，$y = $-1.

答案： 2,-1

5. 方程组$\left\{\begin{array}{l} 3x + 5y = k,\\ 5x + 3y = k\end{array}\right. $中$x$与$y$的和为$2$，则$k = $8.

答案： 8

1. $\left\{\begin{array}{l} \frac{2x - 1}{5} + \frac{3y - 2}{4} = 2,\\ \frac{3x + 1}{5} - \frac{3y + 2}{4} = 0;\end{array}\right. $
解：$\left\{\begin{array}{l} x=3,\\ y=2.\end{array}\right. $

答案： $\left\{\begin{array}{l} x=3,\\ y=2.\end{array}\right. $

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

答案： $\left\{\begin{array}{l} x=7,\\ y=1.\end{array}\right. $