Which system of equations represents the number of students in each program

So based on the problem:
2*mech= elec
3*mech= chem
And the sum of all is 1200
[tex]\begin{gathered} 1200=e+c+m \\ e=2m \\ c=3m \\ 1200=2m+3m+m=6m \\ \frac{1200}{6}=m=200 \end{gathered}[/tex]The answer is the first option