Final answer:
The lines x=2y+17 and x=13+2y do not intersect because they are parallel, having the same slope but different y-intercepts.
Step-by-step explanation:
To determine at what point the lines x=2y+17 and x=13+2y intersect, we set the equations equal to each other because at the intersection, both x-coordinates must be identical. So we have:
2y + 17 = 13 + 2y
Upon simplifying, we notice that the terms involving 'y' cancel each other out, leaving us with 17 = 13, which is not true. This means that the lines do not intersect because they are parallel. For lines to be parallel, they must have the same slope but different y-intercepts, which is the case here as both lines have a slope of 2 and different intercepts (17 and 13, respectively).