Respuesta :
[tex]\begin{gathered} \begin{bmatrix}6r-s+3t=-9 \\ 5r+5s-5t=20 \\ 3r-s+4t=-5\end{bmatrix} \\ \begin{bmatrix}30r-5s+15t=-45 \\ 30r+30s-30t=120 \\ 3r-s+4t=-5\end{bmatrix} \\ 30r+30s-30t=120 \\ - \\ \underline{30r-5s+15t=-45} \\ 35s-45t=165 \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}30r-5s+15t=-45 \\ 35s-45t=165 \\ 3r-s+4t=-5\end{bmatrix} \\ \\ \begin{bmatrix}30r-5s+15t=-45 \\ 35s-45t=165 \\ 30r-10s+40t=-50\end{bmatrix} \\ 30r-10s+40t=-50 \\ - \\ \underline{30r-5s+15t=-45} \\ -5s+25t=-5 \\ \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}30r-5s+15t=-45 \\ 35s-45t=165 \\ -5s+25t=-5\end{bmatrix} \\ \\ \begin{bmatrix}30r-5s+15t=-45 \\ 35s-45t=165 \\ -35s+175t=-35\end{bmatrix} \\ -35s+175t=-35 \\ + \\ \underline{35s-45t=165} \\ 130t=130 \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}30r-5s+15t=-45 \\ 35s-45t=165 \\ 130t=130\end{bmatrix} \\ 130t=130 \\ \frac{130t}{130}=\frac{130}{130} \\ t=1 \end{gathered}[/tex][tex]\begin{gathered} 35s-45\cdot\: 1=165 \\ 35s-45+45=165+45 \\ \frac{35s}{35}=\frac{210}{35} \\ s=6 \end{gathered}[/tex][tex]\begin{gathered} 30r-5\cdot\: 6+15\cdot\: 1=-45 \\ 30r-30+15=-45 \\ 30r-15+15=-45+15 \\ 30r=-30 \\ \frac{30r}{30}=\frac{-30}{30} \\ r=-1 \end{gathered}[/tex]
answer: t=1, s=6, r= -1
