substitution-and-decide-whether-it-is-correct-show-substitutions-and-conclusions

Question

A student solved a system and reported the solution as (x,y)=(−2,4)(x,y) = (−2, 4). The original system was {5x−2y=−18−3x+y=10\begin{cases}5x-2y=-18\ -3x+y=10\end{cases}. Check the student's solution by substitution and decide whether it is correct.

Accepted Answer

Correct: Substitution yields −18=−18−18 = −18 and 10=1010 = 10, so the solution is valid

Answer

Incorrect: The second equation fails after substitution, though the first holds

Answer

Indeterminate: Substitution gives 0=00 = 0, which implies infinitely many solutions, so the reported pair is not unique

Answer

Incorrect: The first equation fails after substitution, although the second holds

A student solved a system and reported the solution as (x,y)=(−2,4)(x,y) = (−2, 4). The original system was {5x−2y=−18−3x+y=10\(\begin{cases}\)5x-2y=-18\\ -3x+y=10\(\end{cases}\). Check the student's solution by substitution and decide whether it is correct.

A student solved a system and reported the solution as $(x, y) = (- 2, 4)$ . The original system was ${\begin{matrix} 5 x - 2 y = - 18 \\ - 3 x + y = 10 \end{matrix}$ . Check the student's solution by substitution and decide whether it is correct.