The line through the points $(1,4),(-5,1)$ intersects the line $4 x+3 y-5=0$ in the point
The line through the points $(1,4),(-5,1)$ intersects the line $4 x+3 y-5=0$ in the point
$(-1,-3)$
$\left(\frac{5}{3}, \frac{-5}{3}\right)$
$(-1,3)$
$(2,1)$
Solution
Equation of line passing through $\mathrm{A}(\mathrm{x}, \mathrm{y})=(1,4)$ and $\mathrm{B}\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(-5,1)$ is
$\begin{array}{l}
\frac{y-4}{4-1}=\frac{x-1}{1+5} \\
\frac{y-4}{3}=\frac{x-1}{6} \Rightarrow 2(y-4)=x-1 \Rightarrow x-1-2 y+8=0 \\
x-2 y+7=0 ...(1)
\end{array}$
Also given equation of line is $4 x+3 y-5=0$ ...(2)
Solving (1) \& (2) we get $x=-1, y=3$