Yes, by comparing the ratios of the coefficients \displaystyle\boldsymbol{\frac{a_1}{a_2}}, \displaystyle\boldsymbol{\frac{b_1}{b_2}}, and \displaystyle\boldsymbol{\frac{c_1}{c_2}}, we can determine the type of solution:

  • If \displaystyle\boldsymbol{\frac{a_1}{a_2} \neq \frac{b_1}{b_2}}, the lines intersect and there is a unique solution.
  • If \displaystyle\boldsymbol{\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}}, the lines are coincident and there are infinitely many solutions.
  • If \displaystyle\boldsymbol{\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}}, the lines are parallel and there is no solution.