A method of making light olefins is described. The method involves producing an alkyne in a pyrolysis process. The alkyne is catalytically hydrogenated in a hydrogenation zone to produce a product stream containing a light olefin. A byproduct stream from the pyrolysis process comprises carbon oxide and hydrogen. The byproduct stream is treated to convert the carbon oxide and the hydrogen to an oxygenated product in a carbon oxide conversion zone, which can then be converted to an olefin in an oxygenate to olefin process.