A system of linear equations is a collection of equations with the same variables. Solutions are the values that satisfy all equations simultaneously.
Solution Methods:
- • Elimination: Add/subtract equations to eliminate variables
- • Substitution: Solve for one variable, substitute into others
- • Cramer's Rule: Use determinants (works when D ≠ 0)
- • Matrix methods: Gaussian elimination, inverse matrices
Types of Solutions:
- • Unique solution: Lines intersect at one point
- • Infinite solutions: Lines are identical
- • No solution: Lines are parallel
Applications:
- • Business: profit/cost analysis
- • Engineering: circuit analysis
- • Economics: supply and demand
- • Physics: force equilibrium
- • Chemistry: mixture problems