Algebraic solutions refer to methods used to find the values of unknown variables in mathematical equations. These solutions often involve manipulating symbols and numbers according to specific rules, allowing for the resolution of equations like linear equations or quadratic equations. In algebra, techniques such as factoring, substitution, and using the quadratic formula are commonly employed to derive solutions. By applying these methods, one can simplify complex problems and determine the values that satisfy the given equations, making algebra a fundamental tool in mathematics and various real-world applications.