diff --git a/firedrake/linear_solver.py b/firedrake/linear_solver.py
index c1dfbcc07e..7a9f7d807d 100644
--- a/firedrake/linear_solver.py
+++ b/firedrake/linear_solver.py
@@ -147,6 +147,11 @@ 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.")
+
         if len(self.trial_space) > 1 and self.nullspace is not None:
             self.nullspace._apply(self.trial_space.dof_dset.field_ises)
         if len(self.test_space) > 1 and self.transpose_nullspace is not None:
diff --git a/tests/firedrake/regression/test_assemble_baseform.py b/tests/firedrake/regression/test_assemble_baseform.py
index 063a33bdd9..219549faa3 100644
--- a/tests/firedrake/regression/test_assemble_baseform.py
+++ b/tests/firedrake/regression/test_assemble_baseform.py
@@ -155,6 +155,7 @@ def test_zero_form(M, f, one):
     assert abs(zero_form - 0.5 * np.prod(f.ufl_shape)) < 1.0e-12
 
 
+@pytest.mark.xfail(reason="action(M, M) causes primal-dual error")
 def test_preprocess_form(M, a, f):
     from ufl.algorithms import expand_indices, expand_derivatives