Section 1. Any county in this State containing a population of not less than five thousand, six hundred (5,600) nor more than five thousand, seven hundred and fifty (5,750) according to the last preceding Federal Census shall have a county unit system of education to the extent specified in this Act, and for the purpose of levying, assessing, and collecting a school equalization tax, and for such other administrative functions as are herein set forth; the territory of each of such counties may be created into a county-wide school district in the manner hereinafter provided and may exercise the taxing power as hereinafter provided. There shall be exercised in and for the entire territory of each of such counties, to the extent in this Act prescribed, the taxing power conferred on school districts by Article 7, Section 3, of the Constitution, but such taxing power shall not be exercised until and unless authorized by a majority of the qualified property taxpaying voters residing therein at an election to be held for that purpose as hereinafter provided.