LINR 3 | Lesson 1 | Explore 3 Solutions

  1. yes
  2. no, they are parallel
  3. yes
  4. yes, same line
  5. Solution to 1:  \((23, 36)\); 3:  \((\frac{2}{3}, \frac{5}{3})\); 4:  Two lines are the same, one of the equations is multiple of the other.
  6. The slopes of number 1 and 4 are different and so the lines intersect.  In number 2 the slopes are the same and in number 4 the slopes are the same, however in 4 the 1st equation is a multiple of the second one.
  7. Rule:  If the slopes are the same the lines but one equation is not the multiple of the other then the lines are parallel.  If the slopes are the same but one equation is the multiple of the other than both equations represent the same line.  If the slopes are not the same they there is a point of intersections.    So a system could have 0 solutions, 1 solution or infinitely many solutions.

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