Solve the following simultaneous equations. \[ \begin{array}{l} \left\{\begin{array}{l} 2 a-2 b=-7 \\ 3 a+5 b=21.5 \end{array}\right. \\ a=\square \\ b=\square \end{array} \]

Step 1 ：Given the system of equations: \[\begin{array}{l} \left\{\begin{array}{l} 2 a-2 b=-7 \\ 3 a+5 b=21.5 \end{array}\right. \end{array}\]

Step 2 ：First, multiply the first equation by 3 and the second equation by 2 to make the coefficients of 'a' in both equations the same: \[\begin{array}{l} \left\{\begin{array}{l} 6 a-6 b=-21 \\ 6 a+10 b=43 \end{array}\right. \end{array}\]

Step 3 ：Subtract the second equation from the first to eliminate 'a': \[-16 b=-64\]

Step 4 ：Solve the equation for 'b': \[b=4\]

Step 5 ：Substitute 'b' into one of the original equations to find the value of 'a': \[a=0.5\]

Step 6 ：The solution to the system of equations is \(a = \boxed{0.5}\) and \(b = \boxed{4}\)