Explanation

Simultaneous equations are solved together to find values satisfying all equations. Methods: substitution (solve one equation for a variable, substitute into other) or elimination (add/subtract equations to remove a variable).

Example: 2x + y = 7, x – y = 2. Adding: 3x = 9, so x = 3. Substituting: 3 – y = 2, so y = 1. Check: 2(3) + 1 = 7 ✓

Graphically, the solution is where lines intersect. Parallel lines (no solution) or same line (infinite solutions) are special cases. Real-world applications include mixture problems and cost analysis.