《2025年桂壮红皮书暑假天地河北少年儿童出版社七年级数学》

1. 下列方程中,是二元一次方程的是(D)
A. $ 2 x - y = z $
B. $ 3 x y + 1 = 0 $
C. $ 0.5 + y = 3 $
D. $ x = 0.5 y $

答案： D

2. 已知$ \left\{ \begin{array} { l } { x = 2, } \\ { y = 1 } \end{array} \right. $是二元一次方程组$ \left\{ \begin{array} { l } { a x + b y = 7, } \\ { a x - b y = 1 } \end{array} \right. $的解,则$ a - b $的值为(A)
A. $ - 1 $
B. $ 1 $
C. $ 2 $
D. $ 3 $

答案： A

3. 若方程组$ \left\{ \begin{array} { l } { 4 x + 3 y = 1, } \\ { a x - ( a - 1 ) y = 3 } \end{array} \right. $的解$ x $与$ y $互为相反数,则$ a $的值为(B)
A. $ 1 $
B. $ 2 $
C. $ 3 $
D. $ 4 $

答案： B

4. 若关于$ x $, $ y $的方程组$ \left\{ \begin{array} { l } { x + y = 3 k, } \\ { x - y = 7 k } \end{array} \right. $的解满足方程$ 2 x + 3 y = 6 $,则$ k $的值为(B)
A. $ - \frac { 3 } { 2 } $
B. $ \frac { 3 } { 2 } $
C. $ - \frac { 2 } { 3 } $
D. $ \frac { 2 } { 3 } $

答案： B

5. 二元一次方程$ 2 x + y = 7 $的正整数解为$\left\{\begin{array}{l} x=1,\\ y=5\end{array}\right.$或$\left\{\begin{array}{l} x=2,\\ y=3\end{array}\right.$或$\left\{\begin{array}{l} x=3,\\ y=1\end{array}\right.$.

答案： $\left\{\begin{array}{l} x=1,\\ y=5\end{array}\right.$或$\left\{\begin{array}{l} x=2,\\ y=3\end{array}\right.$或$\left\{\begin{array}{l} x=3,\\ y=1\end{array}\right.$

6. 已知方程$ 4 x ^ { a + 2 b - 5 } - 2 y ^ { 3 a - b - 3 } = 8 $是二元一次方程,则$ a - b = $0.

答案： 0

7. 甲、乙二人解关于$ x $, $ y $的方程组$ \left\{ \begin{array} { l } { a x + y = 5, } \\ { 2 x - b y = 1, } \end{array} \right. $甲看错$ a $解得$ \left\{ \begin{array} { l } { x = 1, } \\ { y = 1, } \end{array} \right. $乙看错$ b $解得$ \left\{ \begin{array} { l } { x = 1, } \\ { y = 3, } \end{array} \right. $则$ a = $2, $ b = $1;正确的解为$\left\{\begin{array}{l} x=\frac {3}{2},\\ y=2\end{array}\right.$.

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

8. 若$ - 3 x ^ { 2 a - b } y ^ { a + 2 } $和$ 27 x ^ { a + 4 } y ^ { 10 - 3 b } $是同类项,则$ a = $5, $ b = $1.

答案： 5 1

9. 用代入法解方程组:
(1)$ \left\{ \begin{array} { l } { y = 2 x - 3, ① } \\ { 3 x + 2 y = 8 ; ② } \end{array} \right. $
解：$\left\{\begin{array}{l} x=2,\\ y=1\end{array}\right.$
(2)$ \left\{ \begin{array} { l } { 2 x - y = 5, ① } \\ { 3 x + 4 y = 2. ② } \end{array} \right. $
解：$\left\{\begin{array}{l} x=2,\\ y=-1\end{array}\right.$

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

10. 已知$ \left\{ \begin{array} { l } { x = 2, } \\ { y = 1 } \end{array} \right. $是方程组$ \left\{ \begin{array} { l } { 2 x + ( m - 1 ) y = 2, } \\ { n x + y = 1 } \end{array} \right. $的解,求$ m + n $的值.-1

答案： $m+n=-1$