All high schools which have been or may hereafter be established by county boards of education shall constitute a system of high schools for the county. Such high school system shall make provision for the secondary education of all children of the county residing in the territory under the control of the county board of education; provided, that by agreement between county boards of education and city boards of education high schools located in cities or towns of 2,500 or more inhabitants according to the last or any succeeding federal census may be utilized as a part of the high school system of the county, the financial support, administration and supervision of such high schools to be determined by the boards of education involved; and provided further, that in order that the most satisfactory and economic plan of administration may be secured, high schools may, at the discretion of the county board, be designated as a unit in the high school system of the county, with a defined territory or district for patronage, in just the same manner as other public schools under the supervision of county boards of education. Boards of education in cities having a city board of education shall provide a system of high school education which shall meet the minimum standards for high schools authorized and prescribed by the State Board of Education; provided, that any town or city board of education may cooperate with the county board of education in the establishment, support and maintenance of a county system of high schools which shall include the said town or city.