Question

Solve the given system of equations.S =t =-6s+ 3t = - 45-s-5t= -2

Answer 1

`\begin{cases}{-6s+3t=-45} \\ -s-5t={-2}\end{cases}`

1. Solve s in the second equation:

`\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}`

2. Substitute the s in the first equation by the value you get in the previous step:

`-6(2-5t)+3t=-45`

3. Solve t:

`\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=(-33)/(33) \\ \\ t=-1 \end{gathered}`

4. Use the value of t to solve s:

`\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}`Then, the solution of the given system of equations is s=7t= -1