Yes, by comparing the ratios of the coefficients \displaystyle\boldsymbol, \displaystyle\boldsymbol, and \displaystyle\boldsymbol, we can determine the type of solution:

  • If \displaystyle\boldsymbol, the lines intersect and there is a unique solution.
  • If \displaystyle\boldsymbol, the lines are coincident and there are infinitely many solutions.
  • If \displaystyle\boldsymbol, the lines are parallel and there is no solution.