Repeated tilling will kill the grass over a period of a year.
Covering the area
The grass will die within the year if covered completely. Plastic works, but has to be removed before the area can be used. A heavy layer of newspaper eliminates the need for later removal. Hold the newspapers down with material which will compost. It, too, will become part of the soil.
Using corn gluten
Apply corn gluten after tilling. Seedlings can be planted, but seeds should not be sowed for a while. The product is organic and not harmful to pets or children. It is available from Gardens Alive.
If local regulations permit, the area can be burned with the cooperation of the local fire department. That will take care of the shallow lawn grasses, but leave the deep-rooted native prairie grasses. Do not till after the fire. Just start planting. Use mulch to preserve moisture.
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