Answer: It sounds like you need to till again. Whenever you start a garden from lawn or field, you need to contend with the plants you tilled in for several years. Grass roots are tenacious and will sprout new leaves quickly. (You can remove the sod before tilling, but in doing so you lose lots of nutrients and topsoil.) I would till the area again. One option is to lay down black plastic over the tilled area--it's ugly, but it will smother weeds. You can also use landscape fabric. You can plant heat-loving crops like tomatoes and peppers in holes cut into the plastic--just note that you will need to figure out a way to provide water to the plants. Whatever you do, plan to mulch your garden well. You can use grass clippings, straw, or even thick layers of newspapers or corrugated cardboard.
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