How to construct simultaneous equations from two lists?

coefs = {{2, 3, 5}, {1, -1, 0}};

Two additional approaches:

1. Using the fourth argument of Array to do all in a single step:

ClearAll[slv]
slv[a_] := Array[x, Length @ a, 1, Solve[Thread[a. {##, -1} == 0], {##}] &]

slv @ coefs

{{x[1] -> 1, x[2] -> 1}}

2. Process coefs directly into input for LinearProgramming:

ClearAll[lp]
lp[a_] := LinearProgramming[ConstantArray[0, Length@a], Most /@ a, Thread[{Last /@ a, 0}]]

lp @ coefs

{1, 1}

One way might be

 eqs = And @@ Thread[coefs[[1 ;; 2, 1 ;; 2]].vars == coefs[[All, 3]]]

Mathematica graphics

Applying it

coefs = {{2, 3, 5}, {1, -1, 0}};
vars = Array[x, 2];
equ = And @@ Thread[coefs[[1 ;; 2, 1 ;; 2]].vars == coefs[[All, 3]]];
Solve[equ, vars]

Mathematica graphics

If you need to see the equations, use

equ = Thread[coefs.Append[vars, -1] == 0]

Or, just go straight to the solution

Solve[Thread[coefs.Append[vars, -1] == 0], vars]

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