Finding the sum of the first term and common difference when given sum of first 5 and sum of first 10 the sum of the first 5 terms of an arithmetic series is 110 and the sum of the first 10 terms is 320. How do i go about finding the first term and common difference.
Sn  = n/2 [2a+d(n−1)] is the equation for working out the sum of an arithmetic series, but how can i rearrange to find for the first term and common difference. I belive it would be using simulatenous equations.

$\begin{array}{c| cccccccccccccc}
\text{index} & 1 & 2    & 3     &  4    & 5\\
\text{term}  & a & a+d  &  a+2d &  a+3d & a+4d \\
\text{sum}   & a & 2a+d & 3a+3d & 4a+6d & \color{red}{5a+10d=110} \\
\text{formula} &&&&& 5\dfrac{(a)+(a+4d)}{2}
\end{array}$
$\begin{array}{c| cccccccccccccc}
\text{index} & 6      & 7      & 8      &  9     & 10\\
\text{term}  &  a+ 5d &  a+ 6d &  a+ 7d &  a+ 8d & a+9d \\
\text{sum}   & 6a+15d & 7a+21d & 8a+28d & 9a+36d & \color{red}{10a+45d=320}\\
\text{formula} &&&&& 10\dfrac{(a)+(a+9d)}{2}
\end{array}$
\begin{align}
    5a+10d &=110 \\
   10a+45d &=320 \\
\hline
    10a+20d &=220 \\
   10a+45d &=320 \\
\hline
   25d &= 100 \\
\hline
   d &= 4 \\
   a &= 14
\end{align}
