The given matrix equation is:
[tex]\begin{pmatrix}4 & -1 \\ -2 & -1\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}-5 \\ -3\end{pmatrix}[/tex]
To get the required equations, we will have to carry out the matrix multiplication, thus we have:
[tex]\begin{gathered} (4\times x)+(-1\times y)=-5 \\ (-2\times x)+(-1\times y)=-3 \end{gathered}[/tex][tex]\begin{gathered} 4x-y=-5 \\ -2x-y=-3 \end{gathered}[/tex]
Hence, the correct option is option D
