1. Do the lines $x+y-1=0, 2x-5y+1=0$ and $4x-3y-1=0$ pass through the same point?
1. A system of three equations with two unknowns:
$$
\left\{\begin{array}{l}
x+y-1=0, \\
2 x-5 y+1=0 . \\
4 x-3 y-1=0 .
\end{array}\right.
$$

Solving (1) and (2) gives $x=\frac{4}{7}, y=\frac{3}{7}$. Substituting into (3), the equation holds,

Therefore, the three lines intersect at the same point $\left(\frac{4}{7}, \frac{3}{7}\right)$.