diff --git a/firedrake/assemble.py b/firedrake/assemble.py
index 347f2aca90..875d27862e 100644
--- a/firedrake/assemble.py
+++ b/firedrake/assemble.py
@@ -1192,7 +1192,7 @@ def _apply_dirichlet_bc(self, tensor, bc):
         if self._diagonal:
             bc.set(tensor, self._weight)
         elif not self._zero_bc_nodes:
-            # We cannot set primal data on a dual Cofunction, this will throw an error
+            # NOTE this will only work if tensor is a Function and not a Cofunction
             bc.apply(tensor)
         else:
             bc.zero(tensor)
diff --git a/firedrake/linear_solver.py b/firedrake/linear_solver.py
index 7a9f7d807d..7721675a57 100644
--- a/firedrake/linear_solver.py
+++ b/firedrake/linear_solver.py
@@ -147,10 +147,12 @@ def solve(self, x, b):
         if not isinstance(b, (function.Function, cofunction.Cofunction)):
             raise TypeError("Provided RHS is a '%s', not a Function or Cofunction" % type(b).__name__)
 
-        if x.function_space() != self.trial_space or b.function_space() != self.test_space.dual():
-            # When solving `Ax = b`, with A: V x U -> R, or equivalently A: V -> U*,
-            # we need to make sure that x and b belong to V and U*, respectively.
-            raise ValueError("Mismatching function spaces.")
+        # When solving `Ax = b`, with A: V x U -> R, or equivalently A: V -> U*,
+        # we need to make sure that x and b belong to V and U*, respectively.
+        if x.function_space() != self.trial_space:
+            raise ValueError(f"x must be a Function in {self.trial_space}.")
+        if b.function_space() != self.test_space.dual():
+            raise ValueError(f"b must be a Cofunction in {self.test_space.dual()}.")
 
         if len(self.trial_space) > 1 and self.nullspace is not None:
             self.nullspace._apply(self.trial_space.dof_dset.field_ises)