Check with your neighbors and see what they have. Usually rock runs in a layers throughout an area. Depending on different contours, it could be 3" deep at your place but 30" deep at theirs. Depending on the depth, trying to bust through an area as well defined as what you stated might be a bigger issue than what you want to get into.
Bring in a layer of good soil (12+ inches)and make a drought tolerant bed out of that area and plant a few trees around it. It makes a nice look in a yard without the headache of having to water. The root system of drought tolerant plants will sometimes break through the rock and survive for years.
Texas sage, yuccas, salvia greggi, lantana, etc. are some good drought tolerant plants that are perennial.
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I Thes. 5:16-18