diff --git a/experimental/LieAlgebras/src/Util.jl b/experimental/LieAlgebras/src/Util.jl
index 87da4f8f2a7c..65fb4355b0e0 100644
--- a/experimental/LieAlgebras/src/Util.jl
+++ b/experimental/LieAlgebras/src/Util.jl
@@ -24,7 +24,6 @@ function coefficient_vector(M::MatElem{T}, basis::Vector{<:MatElem{T}}) where {T
   for i in 1:nr, j in 1:nc
     rhs[(i - 1) * nc + j, 1] = M[i, j]
   end
-  fl, sol = can_solve_with_solution(lgs, rhs; side = :right)
-  @assert fl
+  sol = solve(lgs, rhs; side = :right)
   return transpose(sol)
 end
diff --git a/experimental/LinearQuotients/src/cox_rings.jl b/experimental/LinearQuotients/src/cox_rings.jl
index 0f1ef2128fff..e92e09690d7f 100644
--- a/experimental/LinearQuotients/src/cox_rings.jl
+++ b/experimental/LinearQuotients/src/cox_rings.jl
@@ -43,8 +43,7 @@ function action_on_basis(G::FinGenAbGroup, G_action::Function, polys::Vector{<:
     # Little bit of a waste to recompute the rref of M all the time.
     # But I don't see how to do it better and mats should not contain many
     # elements anyways.
-    fl, sol = can_solve_with_solution(M, N, side = :left)
-    @assert fl
+    sol = solve(M, N, side = :left)
 
     push!(res, sol)
   end
@@ -140,8 +139,7 @@ function fill_degree!(HBB::HomBasisBuilder, d::Int)
     M = vcat(M, N)
   end
 
-  fl, sol = can_solve_with_solution(V, M, side = :left)
-  @assert fl
+  sol = solve(V, M, side = :left)
 
   # The i-th row of sol gives the coefficient of inhom_gens[row_to_gen[i]] in
   # the basis hom_basisd.
diff --git a/experimental/Rings/QQAbAndPChars.jl b/experimental/Rings/QQAbAndPChars.jl
index 6c3f4edb455f..ff4991eb4188 100644
--- a/experimental/Rings/QQAbAndPChars.jl
+++ b/experimental/Rings/QQAbAndPChars.jl
@@ -44,9 +44,8 @@ end
 function (Chi::PartialCharacter)(b::ZZMatrix)
   @assert nrows(b) == 1
   @assert Nemo.ncols(b) == Nemo.ncols(Chi.A)
-  s = can_solve_with_solution(Chi.A, b, side = :left)
-  @assert s[1]
-  return evaluate(FacElem(Dict([(Chi.b[i], s[2][1, i]) for i = 1:length(Chi.b)])))
+  s = solve(Chi.A, b, side = :left)
+  return evaluate(FacElem(Dict([(Chi.b[i], s[1, i]) for i = 1:length(Chi.b)])))
 end
 
 function (Chi::PartialCharacter)(b::Vector{ZZRingElem})
diff --git a/experimental/SymmetricIntersections/src/representations.jl b/experimental/SymmetricIntersections/src/representations.jl
index 85fc208b7cef..10615d90451a 100644
--- a/experimental/SymmetricIntersections/src/representations.jl
+++ b/experimental/SymmetricIntersections/src/representations.jl
@@ -1316,8 +1316,7 @@ function quotient_representation(rep::LinRep{S, T, U}, M::W) where {S, T, U, W <
   mr = matrix_representation(rep)
   coll = eltype(mr)[]
   for m in mr
-    ok, mm = can_solve_with_solution(proj, m*proj; side=:right)
-    @assert ok
+    mm = solve(proj, m*proj; side=:right)
     push!(coll, mm)
   end
   repQ = _linear_representation(representation_ring(rep), coll)
diff --git a/src/InvariantTheory/affine_algebra.jl b/src/InvariantTheory/affine_algebra.jl
index 0bd6e7984956..354a30cf9c48 100644
--- a/src/InvariantTheory/affine_algebra.jl
+++ b/src/InvariantTheory/affine_algebra.jl
@@ -203,8 +203,7 @@ function relations_primary_and_irreducible_secondary(RG::InvRing)
 
     # Write the products (in N) in the basis of K[V]^G_d given by the secondary
     # invariants (in M)
-    fl, x = can_solve_with_solution(M, N, side = :left)
-    @assert fl
+    x = solve(M, N, side = :left)
 
     # Translate the relations to the free algebra S
     for i = 1:nrows(x)
@@ -308,8 +307,7 @@ function module_syzygies(RG::InvRing)
     monomial_to_column = enumerate_monomials(gens_d)
     M = polys_to_smat(gens_d, monomial_to_column)
     N = polys_to_smat(s_invars_d, monomial_to_column)
-    fl, sol = can_solve_with_solution(M, N, side = :left)
-    @assert fl
+    sol = solve(M, N, side = :left)
 
     for i in 1:length(s_invars_d)
       a = F()