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

Expectations for the Transformation Unit

  • All graphing MUST be done in PENCIL!
  • Use a RULER/STRAIGHT EDGE when drawing lines
  • Once we start Transformations it is your responsibility to MEMORIZE the rules.  They will NOT be given to you on a test or quiz.
  • Look at each day’s lesson when you do your HW, seeing things in color will help!