sol = Solve[{a*x + y == 1, -3*x + b*y == 0}, {x, y}]

NMinimize[Total@Abs[{0.21, 0.34} - sol[[1, ;; , 2]]], {a, b}]

sol := Solve[{a*x + y == 1, -3*x + b*y == 0}, {x, y}];
Minimize[
 {Abs[.21 - x /. sol[[1]]] + Abs[.34 - y /. sol[[1]]],
  1 <= a <= 3 && 1 <= b <= 3}, {a, b}, Integers]