Let's begin by listing out the information given to us:
[tex]\begin{gathered} -x-2y=7----1 \\ 5x-6y=-3---2 \end{gathered}[/tex]
Make variable x the subject of the first equation, we have:
[tex]\begin{gathered} -x-2y=7\Rightarrow-x=7+2y \\ -x=7+2y \\ \text{Multiply through each element by -1, we have:} \\ x=-2y-7----3 \end{gathered}[/tex]
Substitute variable x from the third equation into the second equation, we have:
[tex]\begin{gathered} 5x-6y=-3 \\ x=-2y-7 \\ 5(-2y-7)-6y=-3\Rightarrow-10y-35-6y=-3 \\ -10y-35-6y=-3 \\ \text{Add like terms together, we have:} \\ -10y-6y=-3+35\Rightarrow-16y=32 \\ -16y=32 \end{gathered}[/tex]
Therefore, the correct answer is option C;
