We are looking for the measure of each of the two angles. So let $x$ represent the measure of the larger angle and $y$ represent the measure of the smaller angle. The two angles are supplementary angles, which means the sum of the measures of their angles is $180$ degrees. This gives us one equation for our system: $$x+y=180$$ The measure of the larger angle is $12$ degrees more than three times the smaller angle. This translates into the following equation: $$x=3y+12$$ Hence, our system is as follows: $$\begin{cases} x + y = 180 \\ x = 3y + 12 \end{cases}$$ This system can be easily solved by substitution since the second equation already has $x$ isolated. Thus, the first step in solving this system is to substitute the expression $3y+12$ in place of $x$ in the first equation. This will give us: $$\begin{gathered} (\substitute{3y+12})+y=180\\ 4y+12=180\\ 4y=168\\ y=42 \end{gathered}$$ Therefore, the smaller angle has a measure of $42$ degrees. To find the measure of the larger angle, we can substitute $42$ in place of $y$ in the second equation: $$\begin{gathered} x=3(\substitute{42})+12\\ x=126+12\\ x=138 \end{gathered}$$ Thus, the measure of the larger angle is $138$ degrees. The check is left to the reader.