1. (2024·内蒙古)点$P(x,y)$在直线$y=-\frac {3}{4}x+4$上,坐标$(x,y)$是二元一次方程$5x-6y=33$的解,则点 P 的位置在 (
A. 第一象限
B. 第二象限
C. 第三象限
D. 第四象限
D
)A. 第一象限
B. 第二象限
C. 第三象限
D. 第四象限
答案：D
2. 直线$y=2x$与直线$y=-3x+15$的交点坐标为 (
A. $(3,6)$
B. $(4,3)$
C. $(4,8)$
D. $(2,3)$
A
)A. $(3,6)$
B. $(4,3)$
C. $(4,8)$
D. $(2,3)$
答案：A
3. (2024·秦淮区期末)如图,一次函数$y=\frac {3}{4}x+\frac {9}{2}$的图象与$y=kx+b$的图象相交于点$P(-2,n)$,则关于x,y的方程组$\left\{\begin{array}{l} 3x-4y+18=0,\\ kx-y+b=0\end{array}\right. $的解是 (
A. $\left\{\begin{array}{l} x=-2\\ y=2\end{array}\right. $
B. $\left\{\begin{array}{l} x=-2\\ y=3\end{array}\right. $
C. $\left\{\begin{array}{l} x=3\\ y=-2\end{array}\right. $
D. $\left\{\begin{array}{l} x=2\\ y=-2\end{array}\right. $
A.$\left\{\begin{array}{l} x=-2\\ y=2\end{array}\right. $
B.$\left\{\begin{array}{l} x=-2\\ y=3\end{array}\right. $
C.$\left\{\begin{array}{l} x=3\\ y=-2\end{array}\right. $
D.$\left\{\begin{array}{l} x=2\\ y=-2\end{array}\right. $
B
)A. $\left\{\begin{array}{l} x=-2\\ y=2\end{array}\right. $
B. $\left\{\begin{array}{l} x=-2\\ y=3\end{array}\right. $
C. $\left\{\begin{array}{l} x=3\\ y=-2\end{array}\right. $
D. $\left\{\begin{array}{l} x=2\\ y=-2\end{array}\right. $
A.$\left\{\begin{array}{l} x=-2\\ y=2\end{array}\right. $
B.$\left\{\begin{array}{l} x=-2\\ y=3\end{array}\right. $
C.$\left\{\begin{array}{l} x=3\\ y=-2\end{array}\right. $
D.$\left\{\begin{array}{l} x=2\\ y=-2\end{array}\right. $
答案：B
4. (2024·宝应一模)若关于x,y的二元一次方程组$\left\{\begin{array}{l} y-3x=1,\\ kx-y=0\end{array}\right. $的解是$\left\{\begin{array}{l} x=1,\\ y=4,\end{array}\right. $则一次函数$y=3x+1$与$y=kx$(k是常数,$k≠0$)的图象的交点坐标是____
(1,4)
.答案：(1,4)
5. 如图,直线$l_{1},l_{2}$的交点坐标$(1,3)$可以看作二元一次方程组
$\left\{\begin{array}{l} y=-x+4\\ y=2x+1\end{array}\right.$
的解.答案：$\left\{\begin{array}{l} y=-x+4\\ y=2x+1\end{array}\right.$
6. 如图,直线$l_{1}:y=x+1$与直线$l_{2}:y=mx+n$相交于点$P(1,b).$
(1)求b的值;
(2)不解关于x,y的方程组$\left\{\begin{array}{l} y=x+1,\\ y=mx+n,\end{array}\right. $请直接写出方程组的解;
(3)直线$l_{3}:y=nx+m$是否也经过点 P? 请说明理由.
(1)求b的值;
2
(2)不解关于x,y的方程组$\left\{\begin{array}{l} y=x+1,\\ y=mx+n,\end{array}\right. $请直接写出方程组的解;
$\left\{\begin{array}{l} x=1\\ y=2\end{array}\right.$
(3)直线$l_{3}:y=nx+m$是否也经过点 P? 请说明理由.
直线$l_{3}:y=nx+m$也经过点P.理由如下:∵点P(1,2)在直线$y=mx+n$上，∴$m+n=2$,又$2=n×1+m$,∴直线$l_{3}:y=nx+m$也经过点P.
答案：解:(1)∵点P(1,b)在直线y=x+1上,
∴当x=1时,b=1+1=2.
(2)方程组的解是$\left\{\begin{array}{l} x=1,\\ y=2.\end{array}\right.$
(3)直线y=nx+m也经过点P.理由如下:
∵点P(1,2)在直线y=mx+n上，
∴m+n=2,
又2=n×1+m,∴直线l3:y=nx+m也经过点P.
∴当x=1时,b=1+1=2.
(2)方程组的解是$\left\{\begin{array}{l} x=1,\\ y=2.\end{array}\right.$
(3)直线y=nx+m也经过点P.理由如下:
∵点P(1,2)在直线y=mx+n上，
∴m+n=2,
又2=n×1+m,∴直线l3:y=nx+m也经过点P.