Help using two equations to solve each other

(1) a/2+b=1

(2) 3a-b/3=31/2

Im lost on what to do here. I know I need to pick the easier equation to produce a equaling so I choose equation 1

what im trying to do is first clearing the fractions in eq1 I listed below what my thinking looks like but I know its wrong Please help

a/2+b=1 multiply both a/2 by 2 and the right side by 2 and i get

a+b=2 then I want to find a so I -b

a=2-b

in the second eq i substitute for a now

3a-b/3=31/2

3(2-b)-b/3=31/2 now i clear the brackets

6-3b+b/3=31/2 now i clear the fractions bymultiplying both sides by 3. 3x b/3 and the right side 31/2=15.5 x3

6-3b+b=15.5x3 simplify to

6-3b+b=46.5 now i get the bs alone

-3b+b=40.5 merge the bs

-2b=40.5

-b=40.5/2