Answer: First off, I would never recommend using gasoline as a weed killer! Among a host of reasons, it ruins the soil for any future desirable plant growth. Next, when working the property, be aware that poson ivy can grow as a ground cover, a vine, or in a bush form which can make it hard to recognize; in my (sad) experience, the hairy vine all by itself in addition to the foliage can cause a reaction in sensitized individuals.
To kill poison ivy you can either hand-pull it (wearing adequate protective gear) or very carefully use an herbicide such as glyphosate according to the label instructions. (Glyphosate is an indiscriminate herbicide and will damage all green plants, not just the poison ivy, so read the instructions and be careful if you are working around desirable plants. Use the appropriate formulation listed for poison ivy--sometimes it is called "brush killer" or similar strength.) You can also "smother" poison ivy by cutting it off close to the ground and then covering the area with several layers of newspaper or cardboard followed by a thick layer of mulch. Any one of these approaches may need to be repeated at least once.
Unfortunately, poison ivy is one persistent plant. If you rip out poison ivy, never burn the debris because the smoke will carry the irritant. Also, poison ivy is deciduous and loses its leaves in the winter, but sensitized individuals may still react to the leafless vine.
I hope this helps!
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