A co-extraction system for separating and purifying butadiene and isoprene from a C 4 hydrocarbon mixture comprising butadiene and a C 5 hydrocarbon mixture comprising isoprene, comprising: (a) a C 5 purification column to receive a C 5 hydrocarbon mixture comprising isoprene and separate the light ends of the C 5 hydrocarbon mixture from the heavy ends (C 5 +) hydrocarbons; (b) an extraction zone, comprising: (i) a mainwasher column to receive the light ends of the C 5 hydrocarbon mixture, a C 4 hydrocarbon mixture comprising butadiene, and an extractive solvent, wherein butadiene and isoprene are co-extracted from the C 4 and C 5 hydrocarbon mixtures by using the extractive solvent to provide a crude butadiene product, C 4 acetylenes, and a crude isoprene product; and (ii) a rectifier column to receive the crude butadiene product, the crude isoprene product, the extractive solvent, and the C 4 acetylenes, wherein the crude butadiene product is separated from the crude isoprene product, the extractive solvent, and the C 4 acetylenes; (c) a distillation zone, comprising a butadiene finishing column to receive the crude butadiene product, wherein 1,3-butadiene is purified from the crude butadiene product; (d) a degassing zone, comprising a degasser column to receive the crude isoprene product, the extractive solvent, and the C 4 acetylenes, wherein the extractive solvent is separated from the crude isoprene product and the C 4 acetylenes; and (e) an isoprene finishing column to receive the crude isoprene product and the C 4 acetylenes, wherein isoprene is purified from the crude isoprene product and the C 4 acetylenes. (a) a C 5 purification column to receive a C 5 hydrocarbon mixture comprising isoprene and separate the light ends of the C 5 hydrocarbon mixture from the heavy ends (C 5 +) hydrocarbons; (b) an extraction zone, comprising: (i) a mainwasher column to receive the light ends of the C 5 hydrocarbon mixture, a C 4 hydrocarbon mixture comprising butadiene, and an extractive solvent, wherein butadiene and isoprene are co-extracted from the C 4 and C 5 hydrocarbon mixtures by using the extractive solvent to provide a crude butadiene product, C 4 acetylenes, and a crude isoprene product; and (ii) a rectifier column to receive the crude butadiene product, the crude isoprene product, the extractive solvent, and the C 4 acetylenes, wherein the crude butadiene product is separated from the crude isoprene product, the extractive solvent, and the C 4 acetylenes; (i) a mainwasher column to receive the light ends of the C 5 hydrocarbon mixture, a C 4 hydrocarbon mixture comprising butadiene, and an extractive solvent, wherein butadiene and isoprene are co-extracted from the C 4 and C 5 hydrocarbon mixtures by using the extractive solvent to provide a crude butadiene product, C 4 acetylenes, and a crude isoprene product; and (ii) a rectifier column to receive the crude butadiene product, the crude isoprene product, the extractive solvent, and the C 4 acetylenes, wherein the crude butadiene product is separated from the crude isoprene product, the extractive solvent, and the C 4 acetylenes; (c) a distillation zone, comprising a butadiene finishing column to receive the crude butadiene product, wherein 1,3-butadiene is purified from the crude butadiene product; (d) a degassing zone, comprising a degasser column to receive the crude isoprene product, the extractive solvent, and the C 4 acetylenes, wherein the extractive solvent is separated from the crude isoprene product and the C 4 acetylenes; and (e) an isoprene finishing column to receive the crude isoprene product and the C 4 acetylenes, wherein isoprene is purified from the crude isoprene product and the C 4 acetylenes.