The number of solutions for the equation is determined by the relationship between the constants in the variable expressions on both sides of the simplified equation.
When Robin simplifies both sides of an equation, and the variable expressions on each side have the same coefficient but different constants, the relationship between these constants becomes crucial in determining the number of solutions. If the constants are equal, the equation likely has infinitely many solutions, as the variable terms on both sides will cancel out identically during the simplification process.
On the other hand, if the constants are different, indicating a contradiction, there is no solution to the equation. In this scenario, the constants prevent the variable terms from canceling out, resulting in an inconsistency. Therefore, the number of solutions can be inferred by examining the relative values of the constants in the simplified equation.