69725ebb-their-reasoning-and-determine-whether-their-conclusion-is-valid-show-th

Question

A student attempted to solve the system 5x − 2y = 13 and −10x + 4y = −26 by elimination and concluded there are infinitely many solutions. Examine their reasoning and determine whether their conclusion is valid. Show the algebra.

Accepted Answer

Valid — the second equation is −2 times the first, so the system has infinitely many solutions (dependent equations).

Answer

Valid only if you restrict variables to integers; otherwise no solution exists.

Answer

Invalid — because if you add them you would cancel terms and find a unique solution, so the student made an arithmetic error.

Answer

Invalid — the system is inconsistent and has no solution because multiplication of an equation by a negative scalar creates contradictions.