Where do the lines $x+y=1$ and $6 x-2 y=6$ intersect? Intersection point $=$

Step 1 ：The problem is asking for the intersection point of the lines \(x+y=1\) and \(6x-2y=6\).

Step 2 ：The intersection point of two lines is the point where the two lines meet. This point satisfies the equations of both lines.

Step 3 ：Therefore, to find the intersection point, we need to solve the system of equations formed by the two lines.

Step 4 ：Solving the system of equations \(x + y = 1\) and \(6x - 2y = 6\), we find that the solution is \(x=1\) and \(y=0\).

Step 5 ：This means that the intersection point of the two lines is at \((1,0)\).

Step 6 ：Final Answer: The intersection point of the lines \(x+y=1\) and \(6x-2y=6\) is \(\boxed{(1,0)}\).