- Intersecting Lines
- Different slopes
- The lines intersect at exactly one point. The point is the solution.
- The system is consistent & independent

- Parallel Lines
- Same slope, different y-intercept
- The lines NEVER intersect. There is NO SOLUTION.
- The system is inconsistent

- Coincident Lines
- Same slope, same y-intercept
- The lines intersect at EVERY point. The solution is ALL REAL NUMBERS ON THE LINE.
- The system is consistent & dependent

- Substitution/Elimination
- If you solve an equation and get a value for x or y you MUST find the corresponding value. This means the lines are intersecting
- If you solve the equation and get a contradiction there is no solution. This means the lines are parallel
- If you solve the equation and get an identity the solution is all real numbers on the line. This means the lines are coincident.
- You cannot use elimination unless you have a pair of opposites (2x and -2x). If you do not have a pair of opposites you need to create them by multiplying the entire equation by a number