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1 (2025 无锡锡山期中)给出下列方程:①$x + y = 1$；②$2x - \frac{2}{y} = 1$；③$x^2 + 2x = - 1$；④$5xy = 1$；⑤$x - \frac{1}{3}y = 2$.其中是二元一次方程的是(
A.①⑤
B.①②
C.①④
D.①②④
A
)A.①⑤
B.①②
C.①④
D.①②④
答案
1. A
2 既是方程$x - y = 1$的解，又是方程$2x + y = 5$的解是(
A.$\begin{cases}x = - 1,\\y = 2\end{cases}$
B.$\begin{cases}x = 2,\\y = - 1\end{cases}$
C.$\begin{cases}x = 1,\\y = 2\end{cases}$
D.$\begin{cases}x = 2,\\y = 1\end{cases}$
D
)A.$\begin{cases}x = - 1,\\y = 2\end{cases}$
B.$\begin{cases}x = 2,\\y = - 1\end{cases}$
C.$\begin{cases}x = 1,\\y = 2\end{cases}$
D.$\begin{cases}x = 2,\\y = 1\end{cases}$
答案
2. D
3 (2025 镇江期末)已知关于$x$，$y$的二元一次方程$kx + y = 3 - k$，若当$k$每取一个不为$0$的值时，方程都有一个公共解，则这个公共解为(
A.$\begin{cases}x = - 1,\\y = - 3\end{cases}$
B.$\begin{cases}x = 1,\\y = 3\end{cases}$
C.$\begin{cases}x = - 1,\\y = 3\end{cases}$
D.$\begin{cases}x = 1,\\y = - 3\end{cases}$
C
)A.$\begin{cases}x = - 1,\\y = - 3\end{cases}$
B.$\begin{cases}x = 1,\\y = 3\end{cases}$
C.$\begin{cases}x = - 1,\\y = 3\end{cases}$
D.$\begin{cases}x = 1,\\y = - 3\end{cases}$
答案
3. C
4 (2025 泰州靖江月考)若关于$x$，$y$的方程$2x^{m + 1} + 3y^{n - 1} = 3$是二元一次方程，则$m + 2n$的值为
4
.答案
4. 4
5 (2025 泰州海陵月考)已知$3x + 2 = 2y - x$，用含$x$的代数式表示$y$，则$y =$
$ 2x + 1 $
.答案
5. $ 2x + 1 $
6 (2025 南通如皋期末)若$\begin{cases}x = a,\\y = b\end{cases}$是方程$x - 2y = 0$的解，则$3a - 6b - 3 =$ ______ .
答案
6. $ - 3 $
7 新定义(2025 南通如皋期末)定义：对于任意两个有理数$a$，$b$组成的数对$(a,b)$，我们规定$(a,b) = a + b - 1$，例如：$( - 2,5) = - 2 + 5 - 1 = 2$，则当满足等式$( - 5,3x + 2m) = 6$的$x$是正整数时，$m$的正整数值为
3
.答案
7. 3
8 (2025 连云港东海期中)已知方程组$\begin{cases}3x - y = - 2,\\x - 3y = 10,\end{cases}$则$x + y$等于( )
A.$- 4$
B.$- 6$
C.$2$
D.$4$
A.$- 4$
B.$- 6$
C.$2$
D.$4$
答案
8. B
9 (2025 南通海安期末)已知$x$，$y$满足方程组$\begin{cases}x + m = 3,\\y - 2m = 2,\end{cases}$则$x$，$y$之间的关系式是( )
A.$2x + y = 8$
B.$x + 2y = 7$
C.$x + y = 5$
D.$2x - y = - 5$
A.$2x + y = 8$
B.$x + 2y = 7$
C.$x + y = 5$
D.$2x - y = - 5$
答案
9. A
10 (2025 扬州邗江期末)若关于$x$，$y$的二元一次方程组$\begin{cases}a_1x + b_1y = c_1,\\a_2x + b_2y = c_2\end{cases}$的解是$\begin{cases}x = 2,\\y = 3,\end{cases}$则关于$x$，$y$的二元一次方程组$\begin{cases}2a_1x + b_1y = c_1 + a_1,\\2a_2x + b_2y = c_2 + a_2\end{cases}$的解是( )
A.$\begin{cases}x = \frac{3}{2},\\y = 3\end{cases}$
B.$\begin{cases}x = 2,\\y = 3\end{cases}$
C.$\begin{cases}x = 1,\\y = \frac{3}{2}\end{cases}$
D.$\begin{cases}x = 3,\\y = 2\end{cases}$
A.$\begin{cases}x = \frac{3}{2},\\y = 3\end{cases}$
B.$\begin{cases}x = 2,\\y = 3\end{cases}$
C.$\begin{cases}x = 1,\\y = \frac{3}{2}\end{cases}$
D.$\begin{cases}x = 3,\\y = 2\end{cases}$
答案
10. A
11 (2025 南通如皋期中)若$\begin{cases}x = 2,\\y = 3\end{cases}$是二元一次方程组$\begin{cases}ax - by = 2,\\2ax + 3by = 4\end{cases}$的解，则$a + b$的值为 ______ .
答案
11. 1
