Let [tex]x[/tex] be the number of multiple choice questions and [tex]y[/tex] the number of short-answer questions.
Now,
[tex]\begin{cases}x+y=25\\2x+4y=80\end{cases}[/tex]
Since you only care about finding [tex]y[/tex], you can substitute the first equation into the second to eliminate [tex]x[/tex]. You have
[tex]x+y=25\implies x=25-y[/tex]
and substituting into the other equation,
[tex]2(25-y)+4y=80[/tex]
[tex]50-2y+4y=80[/tex]
[tex]2y=30[/tex]
[tex]y=15[/tex]
