To solve the problem, we notice that both of the equations are written with the y solved then we can equate the expressions of x and solve the resulting equation of x:
![\begin{gathered} x-12=-3x+12 \\ x+3x=12+12 \\ 4x=24 \\ x=(24)/(4) \\ x=6 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/wajz7n0ocgm19wl28u999234cndy2ujjta.png)
Once we have the value of x we plug it on the first equation to find y:
![\begin{gathered} y=6-12 \\ y=-6 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/il0c3cgwkvpvki9pzs2h3m6kcyxz3peh4s.png)
Therefore, the solution of the system of equations is (6,-6)