For the system $\begin{bmatrix}2&-3\\-4&6\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}5\\-10\end{bmatrix}$ which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
Solution of the system:
$2x-3y=5$
$-4x+6y=-10$
Second equation is $-2$ times the first equation.
So both equations represent the same line.
Hence the system is consistent and has infinitely many solutions.
final answer: $\text{(B) and (C)}$