We propose a distributed adaptive algorithm for finding sparse solutions to systems of linear equations. The algorithm is greedy in nature. At each time moment, it first combines the current nonzero elements of the solution received from neighbor nodes by averaging them and then adapts the solution via a coordinate descent update using the local data. The column selection strategy, derived from adaptive matching pursuit, also fuses the received neighbor information with local data. The algorithm provides good performance with limited inter node communication and relatively low computational complexity.