the linear algebraic concept is that the equation becomes underspecified (and tautological in this case) if both sides of the equation simplify to the same terms. if you had two different expressions with a single variable and an max exponent of 1 that were set equal you'd either have 1 solution (the consistent option) or none (the inconsistent option. but you only get multiple solutions if the second expression adds no new information about the value of y.
it's intuitive to jump to simplification but it's good to know why you're applying a specific technique. imagine if there were a follow up question that asked you to specify a third expression that equaled the first two but led to zero solutions. basic simplification won't yield an answer because you need to provide something inconsistent - you get there by fixing one of the two terms and providing a different coefficient for the other.
the linear algebraic concept is that the equation becomes underspecified (and tautological in this case) if both sides of the equation simplify to the same terms. if you had two different expressions with a single variable and an max exponent of 1 that were set equal you'd either have 1 solution (the consistent option) or none (the inconsistent option. but you only get multiple solutions if the second expression adds no new information about the value of y.
it's intuitive to jump to simplification but it's good to know why you're applying a specific technique. imagine if there were a follow up question that asked you to specify a third expression that equaled the first two but led to zero solutions. basic simplification won't yield an answer because you need to provide something inconsistent - you get there by fixing one of the two terms and providing a different coefficient for the other.