# Info About Systems

• 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