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