《2025年暑假乐园现代教育出版社七年级数学人教版》

4. 方程组$\left\{ \begin{array} { l } { x + 2 y = 5, } \\ { 3 x - 2 y = - 1 } \end{array} \right.$的解为$\left\{\begin{array}{l} x = 1,\\ y = 2\end{array}\right.$.

答案： $\left\{\begin{array}{l} x = 1,\\ y = 2\end{array}\right.$

5. 二元一次方程$x + y = 5$的正整数解有$\left\{\begin{array}{l} x = 1,\\ y = 4;\end{array}\right. \left\{\begin{array}{l} x = 2,\\ y = 3;\end{array}\right. \left\{\begin{array}{l} x = 3,\\ y = 2;\end{array}\right. \left\{\begin{array}{l} x = 4,\\ y = 1\end{array}\right.$.

答案： $\left\{\begin{array}{l} x = 1,\\ y = 4;\end{array}\right. \left\{\begin{array}{l} x = 2,\\ y = 3;\end{array}\right. \left\{\begin{array}{l} x = 3,\\ y = 2;\end{array}\right. \left\{\begin{array}{l} x = 4,\\ y = 1\end{array}\right.$

6. 设甲数为$x$，乙数为$y$，根据下列语句，列出二元一次方程或二元一次方程组.
（1）甲数的$3$倍比乙数的$\frac { 1 } { 3 }$大$8$：$3x - \frac{1}{3}y = 8$.
（2）甲数与乙数的差是$6$，且甲数比乙数的$\frac { 1 } { 5 }$大$10$：$\left\{\begin{array}{l} x - y = 6,\\ x - \frac{1}{5}y = 10\end{array}\right.$.

答案：
(1) $3x - \frac{1}{3}y = 8$
(2) $\left\{\begin{array}{l} x - y = 6,\\ x - \frac{1}{5}y = 10\end{array}\right.$

7. 解下列方程组：
（1）$\left\{ \begin{array} { l } { x + 2 y = 9, } \\ { 3 x - 2 y = - 1 ; } \end{array} \right.$
解：$\left\{\begin{array}{l} x = 2\\ y = \frac{7}{2}\end{array}\right.$
（2）$\left\{ \begin{array} { l } { 2 x - y = 5, } \\ { x - 1 = \frac { 1 } { 2 } ( 2 y - 1 ). } \end{array} \right.$
解：$\left\{\begin{array}{l} x = \frac{9}{2}\\ y = 4\end{array}\right.$

答案：
(1) $\left\{\begin{array}{l} x = 2\\ y = \frac{7}{2}\end{array}\right.$
(2) $\left\{\begin{array}{l} x = \frac{9}{2}\\ y = 4\end{array}\right.$

8. 若$3 x ^ { 2 a + b + 1 } + y ^ { a - 2 b - 1 } = 0$是关于$x$，$y$的二元一次方程，求$b - a$的值.

答案： 解：根据题意，得$\left\{\begin{array}{l} 2a + b + 1 = 1,\\ a - 2b - 1 = 1.\end{array}\right.$ 解得$\left\{\begin{array}{l} a = \frac{2}{5},\\ b = -\frac{4}{5}.\end{array}\right.$
所以 $b - a = -\frac{4}{5} - \frac{2}{5} = -\frac{6}{5}$.