[tex]\begin{cases}{-6s+3t=-45} \\ -s-5t={-2}\end{cases}[/tex]
1. Solve s in the second equation:
[tex]\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}[/tex]
2. Substitute the s in the first equation by the value you get in the previous step:
[tex]-6(2-5t)+3t=-45[/tex]
3. Solve t:
[tex]\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=\frac{-33}{33} \\ \\ t=-1 \end{gathered}[/tex]
4. Use the value of t to solve s:
[tex]\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}[/tex]Then, the solution of the given system of equations is s=7t= -1
