Algebra uses letters (variables) to represent unknown quantities. Linear equation: ax + b = 0; solution x = −b/a. Simultaneous equations (two unknowns): solve by substitution or elimination. Quadratic equation: ax² + bx + c = 0. Solutions by: factorisation, completing the square, or quadratic formula x = (−b ± √(b²−4ac)) / 2a. Discriminant b²−4ac: >0 (two real roots), =0 (one repeated root), <0 (no real roots). Inequalities: treat as equation but flip the sign when multiplying/dividing by a negative.