Final answer:
The authority to establish and maintain a free public school system is contained in Article 7 of the Texas Constitution.
Step-by-step explanation:
Article 7 of the Texas Constitution explicitly outlines the state's commitment to education. Section 1 mandates the establishment and maintenance of a free public school system, highlighting its significance for the state. It emphasizes the state's duty to provide for the support and maintenance of an efficient system of public free schools, confirming education as a fundamental right. Additionally, this article touches upon various aspects of education, including funding, administration, and the Permanent School Fund. The Texas Constitution's Article 7 underscores the importance of education as a cornerstone of the state's welfare and progress, reinforcing the government's responsibility to ensure accessible and high-quality education for all Texans.
The correct answer is C. Article 7.