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I need to solve a bunch of systems of n equations in n unknowns where n varies. I can do them, one by one, but I wish to automate the process.

The first equation equals 1 and the rest all equal zero. I currently type in each set of equations manually as follows. I have the n unknowns in a list: list1 = {r,s,...,t}. I have the expressions for the LHS in a 2nd list: list2 = {expr1, ..., exprn}. I write 

sol = Solve[list2[[1]]==1 && list2[[2]]==0 ... && list2[[n]]==0, list1]

I would like to just type Solve[expr, list] where expr is something like 

list2[[1]]==1 && list2[[2]]==0 ... && list2[[n]]==0.

I experimented with Table, RowBox, BoxData, and even CellPrint but I don't know enough to write an expression involving && and == that will work inside the Solve function.

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    $\begingroup$ maybe Solve[Thread[list2==Prepend[ConstantArray[0,Length[list2]-1],1]], list1]? $\endgroup$ – kglr Sep 29 '19 at 3:41
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    $\begingroup$ Solve[First@list2 == 1 && And @@ Thread[Rest@list2 == 0], list1] $\endgroup$ – Bob Hanlon Sep 29 '19 at 5:50
  • $\begingroup$ Both of these work perfectly. Thank you kglr and Bob Hanion. $\endgroup$ – matrixbud Sep 29 '19 at 11:53
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You can try

Solve[Thread[list2 == Prepend[ConstantArray[0, Length[list2] - 1], 1]], list1]
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