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The selvage edges of fabric are sometimes printed, as in this example, and sometimes not as in most batiks. Nevertheless, you should cut them off and not use them in your patchwork piecing. They don't always press flat, and they often pucker and tighten when washed, meaning what they are sewn to doesn't lay flat. They are often thicker to sew through, and longarm quilters often have difficulty quilting through them.
Even though it may be tempting to leave the selvage intact when you are piecing the backing of a quilt, it's best to remove them. I often piece two long lengths of fabric together, matching the selvage edges, but I sew a 1-1/2" seam, using the selvage edge as a guide, and then I cut the selvages off before I press the seam open.
A few years ago using the selvages, particularly those with colored selvage dots, was all the rage.